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Leibniz Universität Hannover

Publication list of Ernst P. Stephan

Books       Articels         Submitted        Converence Procedings

Books (published)

  1. Mathematische Grundlagen der Finiten Element--Methoden. Methoden und Verfahren der mathematischen Physik 23, Lang--Verlag, Frankfurt/M (1982), 207 pp. (with W.L. Wendland)
  2. FEM and BEM--Introduction, Universität Hannover (in German) (1991) 219 pp.\ (with N. Herrmann)
  3. Mathematik und Umwelt (ecological mathematics (in German)), Theodor Oppermann Verlag, Hannover (1994) (with N. Herrmann, J. Siefer, R. Wagner)

Books (in preparation)

  1. Fundamentals of the Finite Element Method (with W.J. Layton)
  2. The Boundary Element Method --- Theory and Application
  3. Numerical Treatment of Boundary Value Problems by First Kind Integral Equations (with J. Gwinner)
  4. Multigrid and Domain Decomposition for Differential and Integral Equations
  5. The hp-Version of the Boundary Element Method --- Theory, Applications and Implementation (with M. Maischak)

Published articels in refereed journals

2010
  1. T. Tran, Q. T. Le Gia, I. H. Sloan, E. P. Stephan: Preconditioners for pseudodifferential equations on the sphere with radial basis functions, Numer. Math. 115 (2010), pp. 141-163
2009
  1. T. Tran, Q. T. Le Gia, I. H. Sloan, E. P. Stephan: Boundary integral equations on the sphere with radial basis functions: error analysis, Appl. Numer. Math. 59 (2009), pp. 2857-2871
  2. M. Maischak, E. Ostermann, E. P. Stephan: TD-BEM for Sound Radiation in three Dimensions and the Numerical Evaluation of Retarded Potentials, NAG/DAGA 2009 - Rotterdam (2009) 633-636
  3. E. P. Stephan: The hp-Version of BEM - Fast Convergence, Adaptivity and Efficient Preconditioning, Journal of Computational Mathematics, 27 (2009), pp. 348-359 
  4. S.A. Funken, E.P. Stephan: Fast solvers with block-diagonal preconditioners for linear FEM-BEM coupling, Numer. Linear Algebra Appl. 16 (2009) 365-395
  5. E. P. Stephan, T. Tran, A. Costea: A boundary integral equation on the sphere for high-precision geodesy. Computer Methods in Mechanics - Lecture Notes on the CMM 2009, edited by Kuczma, Wilmanski, (2009) in print
2008
  1. E.P. Stephan: Efficient Coupling of Finite Elements and Boundary Elements - Adaptive Procedures and Preconditioning, ANZIAM J. 50 (2008) C774-C799
  2. E.P. Stephan, M. Maischak, T. Tran: Domian Decomposition Algorithms for am Indefinite Hypersingular Integral Equation in Three Dimensions, in: Domain Decomposition Methods in Science and Engineering XVII, Lecture Notes in Comp. Sci. and Eng. 60 (2008) 647-655
  3. E. P. Stephan, M. Maischak, E. Ostermann: Transient Boundary Element Method and Numerical Evaluation of Retarded Potentials, Computational Science -- ICCS 2008, Lecture Notes in Computational Science, 5102, pp. 321-330, (2008)
  4. F.-D. Speck, E.P. Stephan: Boundary value problems for the Helmholtz equation in an octant, Integral Eqn. Oper. Theory, 62 (2008), pp. 269-300
  5. G.N. Gatica, M. Maischak, E.P.Stephan: On the coupling of mixed finite element and boundary element methods for a transmission problem with Signorini contact (accepted for publication)
  6. H. Holm, M. Maischak, E. P. Stephan: Exponential convergence of the h-p-version BEM for mixed bvp's on polyhedrons, Math. Meth. Appl. Sci., 31 (2008), pp. 2069-2093
  7. A. Chernov, M. Maischak, E. P. Stephan: hp-mortar boundary element method for two-body contact problems with friction, Math. Meth. Appl. Sci., 31 (2008), pp. 2029-2054
2007
  1. Matthias Maischak, Ernst P. Stephan:The hp-version of the boundary element method for the Lame equation in 3D, in:Boundary Element Analysis,eds.M.Schanz,O.Steinbach,Lecture Notes in Appl. and Comp.Mech.29 (2007) 97-112
  2. A. Chernov, E. P. Stephan: Adaptive BEM for Contact Problems with Friction, Proceedings of the IUTAM, pp.113-122 (2007)
  3. A. Chernov, M. Maischak, E. P. Stephan: A priori error estimates for hp penalty BEM for contact problems in elasticity, Comp. Methods Appl. Mech. Eng. 196, (2007) p. 3871-3880
  4. G. N. Gatica, L.F. Gatica, E. P. Stephan: A dual-mixed finite element method for nonlinear incompressible elasticity with mixed boundary conditions, Comp. Methods Appl. Mech. Eng., 196 (2007), No. 35-36, pp. 3348-3369
  5. N. Heuer, F. Leydecker, E. P. Stephan: An iterative substructuring method for the hp-version of the BEM on quasi-uniform triangular meshes, Num. Methods for PDEs, 23, (2007), 879-903
  6. Krebs, Andreas; Stephan, Ernst P. : A p-version finite element method for nonlinear elliptic variational inequalities in 2D. Numer. Math. 105 (2007), no. 3, 457--480.
  7. Matthias Maischak, Ernst P. Stephan: Adaptive hp-versions of boundary element methods for elastic contact problems, Comput. Mech. 39 (2007)597-607
  8. Ernst P. Stephan, M. Maischak, F. Leydecker: An hp-adaptive finite element/boundary element coupling method for electromagnetic problems, Comput. Mech. 39 (2007)673-680
  9. M. Greiff, M. Maischak, U. B. Bala, W. Mathis, E. P. Stephan: Numerical computation of electric fields including singularities in Mirco Electro Mechanical Systems (MEMS). Przeglad elektrotechniczny, 83(11):47-19, (2007). 14th International Symposium on Theoretical Electrical Engineering, Szczecin, Poland, 20-23, (2007)
2006
  1. A. Chernov, S. Geyn, M. Maischak, E. P. Stephan: Finite element/boundary element coupling for two-body elastoplastic contact problems with friction, in: Analysis and Simulation of Contact Problems, eds. P. Wriggers, U. Nackenhorst, Lecture Notes in Appl. and Comp. Mech. 27 (2006) 171-178
2005
  1. E. P. Stephan, M. Maischak, F. Leydecker: Some Schwarz methods for integral equations on surfaces- h and p versions. Comput. Vis. Sci. 8 (2005), no. 3-4, 211--216.
  2. R. Araya, A. H. Poza, E. P. Stephan: A hierarchical a posteriori error estimate for an advection-diffusion-reaction problem. Math. Models Methods Appl. Sci. 15 (2005), no. 7, 1119-1139.
  3. M. Maischak, E. P. Stephan: Adaptive hp-versions of BEM for Signorini problems, Appl. Numer. Math. 54 (2005), no. 3-4, 425-449.
  4. R. Bustinza, G. Gatica, M. Gonzalez, S. Meddahi and E.P. Stephan: Enriched finite element subspaces for dual-dual mixed formulations in fluid mechanics and elasticity. Computer Methods in Applied Mechanics and Engineering 194 (2005), no. 2-5, 427-439
  5. E. P. Stephan, M. Maischak: A posteriori error estimates for FEM-BEM couplings of three-dimensional electromagnetic problems, Comp. Meth. Appl. Mech. Eng. 194 (2005), no. 2-5, 441-452
  6. M. Maischak, E. P. Stephan: A FEM-BEM coupling method for a nonlinear transmission problem modelling Coulomb Friction Contact, Comp. Meth. Appl. Mech. Eng. 194 (2005), no. 2-5, 453-466
2004
  1. M. Maischak, E.P. Stephan: A Least Squares Coupling Method with Finite Elements and Boundary Elements for Transmission Problems, Computers and Mathematics with Applications 48 (2004), 995-1016.
  2. T. Tran, E. P. Stephan: An overlapping additive Schwarz preconditioner for boundary element approximations to the Laplace screen and Lame crack problems, J. Numer. Math. 12 (2004), no. 4, 311-330
  3. E. P. Stephan: Coupling of Boundary Element Methods and Finite Element Methods, Encyclopedia of Computational Mechanics, Edited by Erwin Stein, René de Borst and Thomas J.R. Hughes. Vol. 1, Chapter 13: Fundamentals. 2004 John Wiley & Sons.
  4. C. Carstensen, M. Maischak, D. Praetorius, E. P. Stephan: Residual-based a posteriori error estimate for hypersingular equation on surfaces, Numer. Math. 97 (2004), no. 3, 397-425
  5. M. Maischak, E. P. Stephan, T. Tran: A multiplicative Schwarz algorithm for the Galerkin boundary element approximation of the weakly singular integral operator in three dimensions, Int. J. of Pure and Appl. Math. (2004), no. 1, 1-21
2003
  1. N. Heuer, E. P. Stephan: An overlapping domain decomposition preconditioner for high order BEM with anisotropic elements, Adv. Comp. Math. (2003), no. 1-3, 211-230
  2. G. N. Gatica, L. F. Gatica, E. P. Stephan: A FEM-DtN formulation for a nonlinear exterior problem in incompressible elasticity, Math. Meth. Appl. Sci. 26 (2003) 151-170
2002
  1. G. Gatica, E. P. Stephan: A mixed-fem formulation for nonlinear incompressible elasticity in the plane, Numer.Meth.Part.Diff.Eqns 18 (2002) 105-128
  2. N. Heuer, M. Mellado, E. P. Stephan, A p-adaptive algorithm for the BEM with the hypersingular operator on the plane screen, Int.J.Numer.Meth.Engng. 53 (2002) 85-104
  3. M. A. Barrientos, G. N. Gatica, E. P. Stephan: A mixed finite element method for nonlinear elasticity: two-fold saddle point approach and a-posteriori error estimate, Numer.Math. 91 (2002) 197-222
2001
  1. N. Heuer, M. E. Mellado, E. P. Stephan, h-p-adaptive two-level methods for boundary integral equations on curves, Computing 67 (2001) 305-334
  2. T. Tran, E. P. Stephan, Two-level additive Schwarz precondioners for the h-p version of the Galerkin boundary element method for 2-d problems, Computing 67 (2001) 57-82
  3. G. N. Gatica, N. Heuer, E. P. Stephan: An implicit-explicit residual error estimator for the coupling of dual-mixed finite elements and boundary elements in elastostatics, Math.Meth.Appl.Sci. 24 (2001), 179-191
  4. N. Heuer, E. P. Stephan, An additive Schwarz method for the h-p version of the boundary element method for hypersingular integral equations in $\mathbb R^3$, IMA J.Numer. Analysis 21 (2001), 265-283
  5. U. Brink, E. P. Stephan: Adaptive coupling of boundary elements and mixed finite elements for incompressible elasticity , Numer.Methods Part.Diff.Equs 17 (2001), 79-92
  6. C. Carstensen, M. Maischak, E. P. Stephan: A posteriori error estimate and h-adaptive algorithm on surfaces for Symm's integral equation, Numer.Math. 90 (2001) 197-213
2000
  1. E. P. Stephan: Multilevel methods for the h-, p- and hp -versions of the boundary element method, J.Comp.Appl.Math. 125 (2000) 503-519
  2. P. Mund, E.P. Stephan: An adaptive two/level method for the hypersingular integral equations in $\mathbb R^3$, ANZIAM J.42(E) (2000) C1019-C1033
  3. M. Maischak, E. P. Stephan, T. Tran: Multiplicative Schwarz algorithms for the Galerkin boundary element method, SIAM J. Numer. Anal. 38 (2000), no.4, 1243 - 1268
  4. T. Tran, E. P. Stephan: Additive Schwarz algorithms for the p version of the Galerkin boundary element method, Numer. Math. 85 (2000), no.3, 433 - 468
  5. E. P. Stephan, T. Tran: Domain decomposition algorithms for indefinite weakly singular integral equations: the h and p versions, IMA J.Numer.Anal 20 (2000), no.1, 1 - 24
1999
  1. P. Mund, E.P. Stephan: An adaptive two-level method for the coupling of nonlinear FEM-BEM equations, SIAM J. Numer. Anal. 36 (1999) 1001-1021
  2. N. Heuer, M. Maischak, E.P. Stephan: Preconditioned Minimum Residual Iteration for the h-p Version of the Coupled FEM-BEM with Quasi-uniform Meshes, Numer. Linear Algebra. Appl. 6 (1999) 435-456
  3. U. Brink. E.P. Stephan: Implicit Residual Error Estimates for the Coupling of Finite Elements and Boundary Elements. Math.Methd.Appl.Sci. 22 (1999) 923-936
  4. N. Heuer, M. Maischak, E.P. Stephan: Exponential Convergence of the h-p-Version for the Boundary Element Method on Open Surfaces. Numer. Math.83 (1999) 641-666
1998
  1. N. Heuer, E.P. Stephan: Iterative substructering for hypersingular integral equations in $\mathbb R^3$. SIAM J. Sci. Comput. 20 (1998) 739-749
  2. N. Heuer, E. P. Stephan: The Poincaré-Steklov operator within countably normed spaces, Mathematical aspects of boundary element methods (Palaiseau, 1998), 152-164, Chapman & Hall/CRC Res. Notes Math., 414, Chapman & Hall/CRC, Boca Raton, FL, 2000
  3. P. Mund, E.P. Stephan, J. Weisse: Two-level methods for the single layer potential in $\mathbb R^3$. Computing 60 (1998) 243-266
  4. T. Tran, E. P. Stephan, S. Zaprianov: Wavelet-based preconditioners for boundary integral equations. Numerical treatment of boundary integral equations, Adv.Comput. Math 9 (1998), no. 1-2, 233-249
  5. P. Mund, E. P. Stephan: The preconditioned GMRES method for systems of coupled FEM-BEM equations. Numerical treatment of boundary integral equations, Adv.Comput.Math. 9 (1998), no. 1-2, 131-144
  6. B. Guo, E. P. Stephan: The h-p version of the coupling of finite element and boundary element methods for transmission problems in polyhedral domains, Numer.Math. 80 (1998), no. 1, 87-107
  7. N. Heuer, E. P. Stephan: Boundary integral operators in countably normed spaces, Math.Nachr. 191 (1998), 123-151
  8. E. P. Stephan, T. Tran: Domain decomposition algorithms for indefinite hypersingular integral equations: the h and p versions, SIAM J.Sci.Comput. 19 (1998), no. 4, 1139-1153 (electronic)
  9. N. Heuer, E. P. Stephan: Preconditioners for the p version of the Galerkinmethod for a coupled finite element/boundary element system, Numer.Methods Partial Differential Equations 14 (1998), no. 1, 47-61
  10. N. Heuer, E. P. Stephan, T. Tran: Multilevel additive Schwarz method for the h-p version of the Galerkin boundary element method, Math.Comp. 67 (1998), no. 222, 501-518
Prior 1998
  1. S. Funken, E.P. Stephan: The BPX preconditioner for the single layerpotential operator. Appl. Anal. 67 (1997) 327-340
  2. M. Maischak, P. Mund, E.P. Stephan: Adaptive multilevel bem for acoustic scattering. Comput.Methods.Appl.Mech.Engrg. 150 (1997) 351-367
  3. J. Elschner, Y.Jeon, I.H. Sloan, E.P. Stephan: Discrete qualocation methods for logarithmic-kernel integral equations on a piecewise smooth boundary.Advances in Computational Math. 7 (1997) 547-571
  4. P. Mund, E.P. Stephan, T. Tran: Hierarchical basis preconditioners for first kind integral equations. Appl. Anal. 65 (1997) 353-372
  5. J. Elschner, Y. Jeon, I.H. Sloan, E.P. Stephan: The collocation method for mixed boundary value problems on domains with curved polygonal boundaries.Numer. Math. 76 (1997) 355-381
  6. P. Mund, E.P. Stephan: Adaptive coupling and fast solution of FEM-BEM equations for parabolic-elliptic interface problems. Math.Meth.Appl.Sci. 20 (1997) 403-423
  7. M. Maischak, E.P. Stephan: The hp-version of the boundary element method in $\mathbb R^3$. The basic approximation results. Math.Meth.Appl.Sci. 20 (1997) 461-476
  8. C. Carstensen, E.P. Stephan: Adaptive boundary element methods for transmission problems, J.Australian Math.Society Series B 38 (1997) 336-367
  9. C. Carstensen, S.A. Funken, E.P. Stephan: On the adaptive coupling of FEM and BEM in 2-d elasticity. Numer. Math. 77 (1997) 187-221
  10. P. Mund, E.P. Stephan: Two-level adaptive boundary element methods for the Laplace, Lamé and Helmholtz equations, In: Proceedings of 1st UK conference on boundary integral methods, Leeds, 30.6.-1.7.1997, 236-245
  11. T. Hartmann, E.P. Stephan: Error analysis for the BEM on nonsmooth curves,In: Boundary Element Topics (1997) 339-350
  12. M. Maischak, E.P. Stephan: The h-p-version of the bem with geometric meshes in 3D, In: Boundary Element Topics (1997) 351-362
  13. S.A. Funken, E.P. Stephan: Fast solvers for non-linear fem-bem equations. In: Proc. IA BEM Symposium on Boundary Element Methods for Nonlinear Problems (ed. W. Wendland, L. Morino), Klower Akad. Publ. Dordrecht, Holland (1996) 63-68
  14. M. Maischak, E.P. Stephan, T. Tran: Domain decomposition methods for boundary integral equations of the first kind: Numerical results Appl.Anal. 63 (1996) 111-132
  15. E.P. Stephan, T. Tran: Localization and post processing for the Galerkin boundary element method applied to three-dimensional screen problems J.Integral Eqns. Appl. 8 (1996) 457-481
  16. C. Carstensen, E.P. Stephan, D. Zarrabi: On the h-adaptive coupling of FE and BE for viscoplastic and elasto-plastic interface problems. J.Comp.Appl.Math. 75 (1996) 345-363
  17. H. Holm, M. Maischak, E.P. Stephan: The hp-version of the boundary element method for Helmholtz screen problems. Computing 57 (1996) 105-134
  18. J. Elschner, E.P. Stephan: A discrete collocation method for Symm's integral equation with corners. J. Comp. Appl. Math. 75 (1996) 131-146
  19. N. Heuer, E.P. Stephan: The h-p version of the boundary element method on polygons. J. Integral Eqns. Appl. 8 (1996) 173-212
  20. C. Carstensen, S.A. Funken, E.P. Stephan: A posteriori error estimates for h-p boundary element methods. Applicable Anal. 61 (1996) 233-253
  21. C. Carstensen, E.P. Stephan: Adaptive boundary element methods for some first kind integral equations, SIAM J.Numer.Anal. 33 (1996) 2166-2183
  22. B. Guo, N. Heuer, E.P. Stephan: The h-p version of the boundary element method for transmission problems with piecewise analytic data, SIAM J.Numer. Anal. 33 (1996) 789-808
  23. E.P. Stephan, T. Tran: Additive Schwarz methods for the h -version boundary element method, Applicable Analysis 60 (1996) 63-84
  24. M. Hahne, E.P. Stephan: Schwarz iteration for the efficient solution of screen problems with boundary elements, Computing 55 (1996) 61-85
  25. E.P. Stephan: The h-p version of the boundary element method for solving 2- and 3-dimensional problems. Comp. Meth. Appl. Mech. Eng. 133 (1996) 183-208
  26. E.P. Stephan: Additive Schwarz methods for integral equations of the first kind, In: MAFELAP 1996, ed. J.R. Whiteman, 123-144
  27. M. Maischak, E.P. Stephan, T. Tran: Two level Schwarz methods for indefinite integral equations, In: DD9 Proceedings, Norway 1996, 504-508
  28. M. Maischak, E.P. Stephan: Schwarz methods for graded meshes in 2D-BEM: numerical results, In: Analysis, Numerics and Applications of Differential and Integral Equations, eds. Constanda, et.al. Proceedings, Stuttgart 1996
  29. S.A. Funken, E.P. Stephan: Hierarchical basis preconditioners for coupled fem-bem equations, In: Proc. 12th GAMM-Seminar, Kiel 1996, Notes in Numerical Fluid Mechanics (ed. W. Hackbusch, G. Wittum)
  30. U. Brink, E.P. Stephan: Convergence rates for the coupling of FEM and collocation BEM. IMA J. Numerical Analysis 16 (1996) 93-110
  31. M. Maischak, E. P. Stephan, T. Tran: Domain decomposition methods for boundary integral equations of the first kind: numerical results, Appl.Anal. 63 (1996), no. 1-2, 111-132
  32. H. Holm, E.P. Stephan: A boundary element method for electromagnetic transmission problems. Applicable Analysis 56 (1995) 213-226
  33. C. Carstensen, E. P. Stephan: Adaptive coupling of boundary and finite element methods, Math. Modelling Num. Analysis 29 (1995) 779-817
  34. C. Carstensen, E. P. Stephan: A posteriori error estimates for boundary element methods. Math. Comp. 64 (1995) 483-500
  35. C. Carstensen, E. P. Stephan: Coupling of finite element and boundary element method for a nonlinear interface problem: The h-p-version, Numer. Methods Part. Diff. Eqns 11 (1995) 539-554
  36. C. Carstensen, E. P. Stephan: Interface problems in elasto-viscoplasticity, Quarterly of Appl. Math. III (1995) 633-655
  37. C. Carstensen, D. Estep, E. P. Stephan: h-adaptive boundary element schemes, Comp. Mechanics 15 (1995) 372-383
  38. M. Hahne, E. P. Stephan, W. Thies: Fast solvers for coupled FEM - BEM equations I -- In: Fast Solvers for Flow Problems, ed. W. Hackbusch, G.Wittum, Notes on Numerical Fluid Mechanics 49 (1995) 121-130
  39. T. Hartmann, E.P. Stephan: Rates of convergence for collocation with Jacobi polynomials for the airfoil equation. J.Comp.Appl.Math. 51 (1994) 179-191
  40. N. Heuer, E.P. Stephan: The hp-version of the boundary element method. ZAMM (1994) T511-T513
  41. M. Costabel, V.J. Ervin, E.P. Stephan: Quadrature and collocation methods for the double layer potential on polygons, Zeitschrift für Analysis und ihre Anwendungen 12 (1993) 699-707
  42. J. Gwinner, E.P. Stephan: A boundary element procedure for contact problems in plane linear elastostatics, RAIRO Math.Mod.Num.Anal. 27 (1993) 457-480
  43. V.J. Ervin, N. Heuer, E.P. Stephan: On the h-p version of the Boundary Element Method for Symms's Integral Equation on Polygons, Comp.Meth. in Applied Mechanics Eng. 110 (1993) 25-38
  44. V.J. Ervin, E.P. Stephan: Adaptive approximations for 3-D electrostatic plate problems, Advances in Engineering Software 15 (1992) 211-215)
  45. V.J. Ervin, E.P. Stephan: Collocation with Chebyshev Polynomials for a hypersingular integral equation on an interval, J.Computational Applied.Math. 43 (1992) 221-229
  46. E.P. Stephan: Coupling of finite elements and boundary elements for some nonlinear interface problems, Computer Methods in Applied Mechanics and Engineering 101 (1992) 61-72
  47. I. Sloan, E.P. Stephan: Collocation with Chebyshev polynomials for Symm's Integral Equation on an Interval, J. Australian Math. Society Series B 34 (1992) 199-211
  48. T. von Petersdorff, E.P. Stephan: Multigrid solvers and preconditioners for first kind integral equations, Numer.Meth.Part.Diff.Eqns. 8 (1992) 443-450
  49. T. von Petersdorff, E.P. Stephan: Singularities of the solution of the Laplacian in domains with circular edges, Applicable Analysis 45 (1992) 281-294
  50. E.P. Stephan, M. Suri: The h-p version of the boundary element method on polygonal domains with quasiuniform meshes, Mathematical Modelling Numerical Analysis M AN RAIRO Analy.Numer. 25 (6) (1991) 783-807
  51. M. Costabel, V.J. Ervin, E.P. Stephan: Experimental convergence rates for various couplings of boundary and finite elements, Mathl.Comput.Modelling 15 (1991) 93-102
  52. V.J. Ervin, E.P. Stephan: A boundary element method with mesh refinement for a weakly singular integral equation, Communications in Applied Numerical Methods 7 (1991) 273-280
  53. G.C. Hsiao, E.P. Stephan, W.L. Wendland: On the Dirichlet problem in elasticity for a domain exterior to an arc, J.Computational and Applied Mathematics 34 (1991) 1-19
  54. E.P. Stephan, W.L. Wendland: A hypersingular boundary integral method for two-dimensional screen and crack problems, Arch.Rational Mech.Anal 112 (1990) 363-390
  55. S. Abou El-Seoud, V.J. Ervin, E.P. Stephan: An improved boundary element Galerkin method for the charge density of a thin, electrified, square plate in $\mathbb R^3$, Math.Meth. in Appl.Sciences 13 (1990) 291-303
  56. V.J. Ervin, E.P. Stephan: A boundary element Galerkin method for a hypersingular integral equation on open surfaces, Math.Meth. in Appl. Sciences 13 (1990) 281-289
  57. F.V. Postell, E.P. Stephan: On the h, p and h-p version of the boundary element method - Numerical results, Computer Methods in Applied Mechanics Engineering 83 (1990) 69-89
  58. I. Babuska, B.Q. Guo, E.P. Stephan: The h-p version of the boundary element method with geometric mesh on polygonal domains, Computer Methods in Applied Mechanics and Engineering 80 (1990) 319-325
  59. T. von Petersdorff, E.P. Stephan: On the convergence of the multigrid method for a hyper-singular integral equation of the first kind, Numerische Mathematik 57 (1990) 379-391
  60. I. Babuska, B. Guo, E.P. Stephan: On the exponential convergence of the h-p version for boundary element Galerkin methods on polygons, Math.Methods in Applied Sciences 12 (1990) 413-427
  61. M. Costabel, V.J. Ervin, E.P. Stephan: Experimental asymptotic convergence of the collocation method for the boundary integral equations on polygons, governing Laplace's equation, Journal of Computational Mechanics 6 (1990) 271-278
  62. E.P. Stephan: A boundary integral equation procedure for the mixed boundary value problem of the vector Helmholtz equation, Applicable Analysis 35 (1990) 59-72
  63. T.von Petersdorff, E.P. Stephan: Decompositions in edge and corner singularities for the solution of the Dirichlet problem of the Laplacian in a polyhedron, Mathematische Nachrichten 149 (1990) 71-104
  64. T.von Petersdorff, E.P. Stephan: Regularity of mixed boundary value problems in $\mathbb R^3$ and boundary element methods on graded meshes, Mathematical Methods in Applied Sciences 12 (1990) 229-249
  65. M. Costabel, V.J. Ervin, E.P. Stephan: Symmetric coupling of finite elements and boundary elements for a parabolic-elliptic interface problem, Quarterly of Applied Mathematics 48 (1990) 265-279
  66. M. Costabel, E.P. Stephan: Integral equations for transmission problems in linear elasticity, Journal of Integral Equations and Applications 2 (1990) 211-223
  67. M. Costabel, E.P. Stephan: Coupling of Finite Element and Boundary Element Methods for an Elasto-Plastic Interface Problem, SIAM Numerical Analysis 27 (1990) 1212-1226
  68. E.P. Stephan, M. Suri: On the convergence of the p-version for some boundary element Galerkin methods, Mathematics of Computation 52 (1989) 31-48
  69. M. Costabel, E.P. Stephan: Duality estimates for the numerical approximation of boundary integral equations, Numerische Mathematik 54 (1988) 339-353
  70. M. Costabel, E.P. Stephan: Strongly elliptic boundary integral equations for electromagnetic transmission problems, Proc.Royal Society Edinburgh 109A (1988) 271-296
  71. M. Costabel, V.J. Ervin, E.P. Stephan: On the convergence of collocation methods for Symm's integral equation on open curves, Mathematics of Computation 51 (1988) 167-179
  72. E.P. Stephan, J.R. Whiteman: Singularities of the Laplacian at corners and edges of three dimensional domains and their treatment with finite element methods, Math.Meth. in Appl.Sciences 10 (1988) 339-350
  73. E.P. Stephan, M. Suri: A p-version boundary element method for screen and crack problems, Ramanujan Birth Centenary International Symposium on Analysis, Pune, India (1987)
  74. M. Costabel, E.P. Stephan: On the convergence of collocation methods for boundary integral equations on polygons, Mathematics of Computation 49 (1987) 461-478
  75. M. Costabel, E.P. Stephan: An improved boundary element Galerkin method for threedimensional crack problems, Journal of Integral Equations and Operator Theory 10 (1987) 467-504
  76. E.P. Stephan: Boundary integral equations for screen problems in $\mathbb R^3$, Journal of Integral Equations and Operator Theory 10 (1987) 236-257
  77. E.P. Stephan: Boundary integral equations for mixed boundary value problems in $\mathbb R^3$, Math.Nachrichten 134 (1987) 21-53
  78. E.P. Stephan: Boundary integral equations for magnetic screens in $\mathbb R^3$, Proc.Royal Soc.Edinburgh 102 A (1986) 189-210
  79. E.P. Stephan: A boundary integral equation method for three-dimensional crack problems in elasticity, Math.Meth. in the Appl.Sciences 8 (1986) 609-623
  80. G.J. Fix, E.P. Stephan: On the Finite Element-Least Squares Approximation to Higher Order Elliptic Systems, Archive Rat.Mech.Anal. 91 (1986) 137-151
  81. R.C. MacCamy, E.P. Stephan: A skin effect approximation for eddy current problems, Archive Rat.Mech.Anal. 90 (1985) 87-98
  82. M. Costabel, E.P. Stephan: A direct boundary integral equation method for transmission problems, Journal of Mathematical Analysis and Applications 106 (1985) 367-413
  83. E.P. Stephan, W.L. Wendland: An augmented Galerkin procedure for the boundary integral method applied to mixed boundary value problems, Applied Numerical Mathematics 1 (1985) 121-143
  84. E.P. Stephan W.L. Wendland: An augmented Galerkin procedure for the boundary integral method applied to two-dimensional screen and crack problems, Appl.Analysis 18 (1984) 183-219
  85. U. Lamp, T. Schleicher, E.P. Stephan, W.L. Wendland: Galerkin collocation for an improved boundary element method for a plane mixed boundary value problem, Computing 33 (1984) 269-296
  86. M. Costabel, E.P. Stephan: Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation, Mathematical Models and Methods in Mechanics, Banach Center Publications, Warsaw 15 (1985) 175-251
  87. R.C. MacCamy, E.P. Stephan: Solution procedures for three-dimensional eddy current problems, Journal Math.Anal. and Appl. 101 (1984) 348-379
  88. M. Costabel, E.P. Stephan: Boundary integral equations for Helmholtz transmission problems and Galerkin approximation, ZAMM 64 (1984) T356-T358
  89. S. Hariharan, E.P. Stephan: A boundary element method for a two-dimensional interface problem in electromagnetics, Numerische Mathematik 42 (1983) 311-322
  90. M. Costabel, E.P. Stephan, W.L. Wendland: On Boundary Integral Equations of the First Kind for the bi-Laplacian in a Polygonal Plane Domain, Annali Scuola Normale Superiore Pisa, Ser. IV 10 (1983) 197-241
  91. M. Costabel, E.P. Stephan: The normal derivative of the double layer potential on polygons and Galerkin approximation, Applicable Analysis 16 (1983) 205-228
  92. R.C. MacCamy, E.P. Stephan: A boundary element method for an exterior problem for three-dimensional Maxwell's equations, Applicable Analysis 16 (1983) 141-163
  93. M. Costabel, E.P. Stephan: Curvature terms in the asymptotic expansions for solutions of boundary integral equations on curved polygons, Journal Integral Equations 5 (1983) 353-371
  94. J. Bielak, E.P. Stephan: A modified Galerkin procedure for bending of beams on elastic foundations, SIAM Journal on Scientific and Statistical Computing 4 (1983) 340-352
  95. E.P. Stephan, W.L. Wendland: Boundary Element Method for Membrane and Torsion Crack Problems, Comput.Meth.Appl.Mech.Eng. 36 (1983) 331-358
  96. G. Fix and E. Stephan, Finite Element Methods of Least-Squares Type for Regions with Corners, ICASE report 81--41, NASA Langley Research Center, Hampton, VA (1981)
  97. E.P. Stephan: Conform and Mixed Finite Element Schemes for the Dirichlet Problem for the Bilaplacian in Plane Domains with Corners, Math.Meth. in Appl.Sci. 1 (1979) 354-382
  98. G.C. Hsiao, E.P. Stephan, W.L. Wendland: On the Integral Equation Method for the Plane Mixed Boundary Value Problem of the Laplacian, Math.Meth. in Appl.Sci. 1 (1979) 265-321
  99. E.P. Stephan, V. Weissgerber: Zur Approximation von Schalen mit hybriden Elementen, Computing 20 (1978) 75-94
  100. E. P. Stephan: Difference approximations for some pseudodifferential equations in $\mathbb R^3$, Ordinary and partial differential equations, Lecture Notes in Math., Vol. 564 (1976) 452-460
  101. E.P. Stephan: Differenzenapproximationen von Pseudo-Differentialgleichungen, Z. Angew. Math. Mech. 56 (1976), no.3, T267-T268
  102. E.P. Stephan, W.L. Wendland: Remarks to Galerkin and Least Squares Methods with Finite Elements for General Elliptic Problems, manuscripta geodaetica 1 (1976) 93-123

Accepted for publication

  1. T. von Petersdorff, E.P. Stephan: A multigrid method on graded meshes for a hypersingular integral equation, Numer.Math.
  2. E.P. Stephan, A. Wathen: Convergence of preconditioned minimum residual iteration for coupled finite element / boundary element computations. SIAMJ.Numer.Anal.
  3. M. Hahne, M. Maischak, E.P. Stephan, A. Wathen: Efficient preconditioners for coupled FEM - BEM equations. Numer.Meth.Part.Diff.Eqns.

Submitted

  1. A. Chernov, S. Geyn, M. Maischak, E. P. Stephan: FE/BE coupling for thermoelastic contact problems
  2. A. Chernov, S. Geyn, M. Maischak, E. P. Stephan: Boundary element procedures for elastorplastic contact problems.
  3. M. Teltscher, E. P. Stephan, M. Maischak: A residual error estimator for an electromagnetic fem-bem coupling problem in R3 (2003)
  4. M. Teltscher, E. P. Stephan, M. Maischak: A hierarchical error estimator for an eddy current fem-bem coupling problem in R3 (2003)
  5. M. Teltscher, E. P. Stephan, M. Maischak: A hierarchical error estimator for an electromagnetic scattering problem coupling fem and bem in R3 (2003)
  6. R. Araya, P. Le Tallec, E. P. Stephan: A hierarchical a-posteriori error estimate for nonlinear incompressible elasticity in the plane (2003)
  7. M. Maischak, E.P. Stephan: The h-p-version of the boundary element method in R3 .Part II: Approximation results for the countably normed spaces
  8. S.A. Funken, E.P. Stephan: Fast solvers with multigrid preconditioners for linear FEM-BEM coupling
  9. A. Krebs, M. Maischak, E. P. Stephan: The p-version for a one-dimensional contact problem
  10. A. Krebs, M. Maischak, E. P. Stephan: Adaptive FEM-BEM coupling with a Schur complement error indicator
  11. E.P. Stephan, T. Tran: An overlapping additive Schwarz preconditioner for boundary element approximations to the Laplace screen and Lamé crack problems
  12. G. Gatica, M. Maischak, E.P. Stephan: Mixed FEM and BEM coupling for a transmission problem with Signorini contact

Publications in Conference Proceedings (Ernst P. Stephan)

  1. M. Maischak, E. Ostermann, E. P. Stephan: Efficient quadrature of retarded potentials, Oberwolfach Report, 2008
  2. E. P. Stephan, S. Geryn, M. Maischak, M. Andres: A boundary element / finite element procedure for metal chipping, CMM-2007 Computer Methods in Mechanics, Lodz, Poland 2007
  3. E. P. Stephan, M. Maischak: Adaptive mixed finite element methods for nonlinear elasticity: a two-fold saddle point approach, WCCM VI 2004, Beijing, Proceedings, 7 pp.
  4. E.P. Stephan, M. Maischak, F. Leydecker: hp-adaptive boundary element method for electromagnetic problems, ECCOMAS 2004, Jyväskylä, Proceedings, 9 pp.
  5. M. Maischak, E.P. Stephan: Adaptive hp-versions of boundary element methods for elastic contact problems, ECCOMAS 2004, Jyväskylä, Proceedings, 18 pp.
  6. R. Araya, A. Poza, E.P. Stephan: A hierarchical a posteriori error estimate for an advection-diffusion-reaction problem, ECCOMAS 2004, Jyväskylä, Proceedings, 19 pp.
  7. E. P. Stephan, M. Maischak, F. Leydecker, S. Oestmann: On the hp-Version BEM for First Kind Integral Equations on Surfaces - Error Analysis, Adaptivity, Preconditioners, In: 5th World Congress on Computational Mathematics, Vienna, Austria, 2002
  8. Additive Schwarz methods for integral equations of the first kind, In: MAFELAP 1996, ed. J.R. Whiteman
  9. Error analysis for the BEM on nonsmooth curves, In: Boundary Element Topics, W.L. Wendland (Editor), Springer 1998 (with T. Hartmann)
  10. The h-p-version of the bem with geometric meshes in 3D, In: Boundary Element Topics, W.L. Wendland (Editor), Springer 1998 (with M. Maischak)
  11. Hierarchical basis preconditioners for coupled fem-bem equations (with S.A. Funken), In: Proc. 12th GAMM-Seminar, Kiel 1996, Notes in Numerical Fluid Mechanics (ed. W. Hackbusch, G. Wittum)
  12. Fast solvers for non-linear fem-bem equations. In: Proc. IABEM Symposium on Boundary Element Methods for Nonlinear Problems (ed. W. Wendland, L. Morino), Klower Akad. Publ. Dordrecht, Holland (1996) 63-68 (with S.A. Funken)
  13. The h-p version of the boundary element method, In: Proc. Conference BEM-15, 1993, Worcester, USA. Advances in Boundary Elements, ed. Brebbia, C.A.
  14. Boundary element convergence for a variational inequality of the second kind. In: Parametric Optimization and Related Topics III (ed. J. Guddat, H.Th. Jongen, B. Kummer, F. Noziska (eds.)) Reihe Approximation + Optimization Vol. 3 Verlag Peter Lang, Frankfurt 1993, 227-241 (with J. Gwinner)
  15. Collocation with Chebyshev polynomials for first kind integral equations on intervals. In Mafelap VII (1990) 321-329 ed. J.R. Whiteman (with V.J. Ervin)
  16. An h-p version of boundary element method for plane mixed boundary value problems. In Proc. Conference BEM-11, 1989, Cambridge, USA (1989) (with B. Guo, T. von Petersdorff). Advances in Boundary Elements, Vol I, ed. Brebbia, C.A., Connor, J.J. (1989) 95-103
  17. The h-p version of the boundary element method with geometric mesh on polygonal domains. In ICOSAHOM '89, International Conference on Spectral and Higher Order Methods for Partial Differential Equations, Como, Italy (1989) (with I. Babuska, B. Guo)
  18. Improved Galerkin methods for integral equations on polygons and on polyhedral surfaces. Japan-U.S. Symposium on Boundary Element Methods, Tokyo, (1988) 73-80
  19. The h-p version of the Galerkin boundary element method for integral equations on polygons and open arcs. In Proc. Conference BEM-10, 1988. Southampton (ed. C.A. Brebbia) pp. 205-216
  20. An h-p method with quasiuniform mesh for integral equations on polygons. In ICES Conference 1988, Atlanta (ed. S. Atluri), Computational Mechanics '88, Vol. 1, pp. 5.iv. 1-5.iv.5, Springer, Berlin (with M.S. Suri)
  21. A direct boundary element method for interface crack problems. In Proc. ICES Conference 1988, Atlanta (ed. S. Atluri) (with T. von Petersdorff). Computational Mechanics '88, Vol. 1, pp. 11.vii.1-11.vii.5, Springer, Berlin
  22. Boundary element methods for some 3D screen problems. In ICES Conference 1988 Atlanta (ed. S. Atluri). Computational Mechanics '88, Vol. 1, pp. 5.ii.1-5.ii.5, Springer, Berlin (with V.J. Ervin)
  23. Experimental convergence of boundary element methods for the capacity of the electrified square plate. Boundary Element Methods in Engineering, ed. C.A. Brebbia, W.L. Wendland, Springer-Verlag, Berlin, 1987 (with V.J. Ervin)
  24. Coupling of finite elements and boundary elements for transmission problems of elastic waves in IR3. In Advanced Boundary Element Methods, IUTAM Symposium 1987, San Antonio, ed. T.A. Cruse, Springer-Verlag, Berlin, 1988, 117-124 (with M. Costabel)
  25. Coupling of finite elements and boundary elements for inhomogeneous transmission problems in IR3. In MAFELAP IV 1987, ed. J.R. Whiteman, Academic Press, London, 1988, 289-296 (with M. Costabel)
  26. A Galerkin method for a three-dimensional time dependent interface problem in electromagnetics, Proceed. Workshop in Electromagnetics-Magnetostatics, INRIA, Rocquencourt, France (1987)
  27. Collocation methods for integral equations on polygons, in: Innovative Numerical Methods in Engineering, ed. R.P. Shaw et al, Proceed. 4th International Symposium, Georgia Tech, Atlanta, GA, 1986, Springer Verlag, Berlin, New York (1986) 43-50 (with M. Costabel)
  28. A boundary element method for three-dimensional crack problems, in: Innovative Numerical Methods in Engineering, ed. R.P. Shaw et al., Proceed. 4th International Symposium, Georgia Tech, Atlanta, GA, 1986, Springer Verlag, Berlin, New York (1986) 351-359 (with M. Costabel)
  29. The boundary integral method for two-dimensional screen and crack problems, Boundary Element Methods in Engineering, BEM 84, ed. C.A. Brebbia, Springer Verlag, Berlin, 1984, 16 pages (with W. Wendland)
  30. The method of Mellin transformation for boundary integral equations on curves with corners, Numerical Solution of Singular Integral Equations (ed. A. Gerasoulis, R. Vichnevetsky) IMACS, 95-102 (1984) (with M. Costabel)
  31. An integral equation formulation for a boundary value problem of elasticity in the domain exterior to an arc. Proceeding of Oberwolfach Conference on Singularities, (eds. P. Grisvard, W.L. Wendland, J.R. Whiteman), 1984, 13 pages (with G.C. Hsiao and W. L. Wendland)
  32. Solution procedure for interface problems in acoustics and electro-magnetics. CISM Courses and Lectures No. 277, ed. P. Filippi, (1983), 291-348
  33. Zur Randintegralmethode für das erste Fundamentalproblem der ebenen Elastizitätstheorie auf Polygongebieten. (On the boundary integral method for the first fundamental problem in elasticity on polygonal domains). In: Recent Trends in Mathematics, Conference in Reinhardsbrunn October 1982, Teubner-Texte zur Mathematik 50 (1982) 56-68 (with M. Costabel and W.L. Wendland)
  34. Theoretical and experimental asymptotic convergence of the boundary integral method for a plane mixed boundary value problem, Boundary Element Methods in Engineering, ed. A. Brebbia, Springer Verlag, Berlin, 1982, 3-17 (with U. Lamp, T. Schleicher and W.L. Wendland)
  35. A simple layer potential method for three-dimensional eddy current problems, in Ordinary and Partial Differential Equations, Dundee (1982) (ed. by W.N. Everitt and B.D. Sleeman), Lecture Notes in Mathematics Vol. 964 Springer Verlag, Berlin, 1982, p. 477-484 (with R.C. MacCamy)
  36. The boundary integral method for a mixed boundary problem in a polygonal domain. Advances in Computer Methods for Partial Differential Equations-IV, IMACS, 300-304 (1981) (with M. Costabel)
  37. The boundary integral method for a plane mixed boundary value problem. Advances in Computer Methods for Partial Differential Equations-IV, IMACS 223-229 (1981) (with U. Lamp, K.T. Schleicher, W.L. Wendland)
  38. Boundary integral methods for mixed boundary value problems. In: ed. R. Shaw et al. Innovative Numerical Analysis for the Engineering Sciences, University Press of Virginia, Charlottesville 1980, 543-554 (with W.L. Wendland)

 
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