Mathematische Grundlagen der Finiten Element--Methoden. Methoden und Verfahren der mathematischen Physik 23, Lang--Verlag, Frankfurt/M (1982), 207 pp. (with W.L. Wendland)
FEM and BEM--Introduction, Universität Hannover (in German) (1991) 219 pp. (with N. Herrmann)
Mathematik und Umwelt (ecological mathematics (in German)), Theodor Oppermann Verlag, Hannover (1994) (with N. Herrmann, J. Siefer, R. Wagner)
Modelling, Simulation and Software Concepts for Scientific-Technological Problems, Lecture Notes in Applied and Computational Mechanics 57, Springer (2011) (with P. Wriggers)
Advanced Boundary Element Methods - Treatment of Boundary Value, Transmission and Contact Problems (with J. Gwinner) Springer Series of Computational Mathematics Vol 52, 2018
Books (in preparation)
Fundamentals of the Finite Element Method (with W.J. Layton)
The Boundary Element Method --- Theory and Application
Multigrid and Domain Decomposition for Differential and Integral Equations
The hp-Version of the Boundary Element Method --- Theory, Applications and Implementation (with M. Maischak)
Published articels in refereed journals
2021
H. Gimperlein, M. Maischak, E. P. Stephan, FE–BE coupling for a transmission problem involving microstructure, Journal of Applied and Numerical Optimization 3 (2021), 315-331
E. P. Stephan, T. Tran, Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods, Springer, 589 pages.
L. Banz, M. Ilyas, B.P. Lamichhane, W. McLean, E. P. Stephan, A mixed finite element method for the Poisson problem using biorthogonal system with Raviart-Thomas elements, Num. Method Part. Diff. Eq. 37 (2021), 2429-2445.
2020
H. Gimperlein, C. Özdemir, D. Stark, E. P. Stephan, A residual a posteriori error estimate for the time-domain boundary element method, Numerische Mathematik 146 (2020), 239-280.
H. Gimperlein, C. Özdemir, E. P. Stephan, A time-dependent FEM-BEM coupling method for fluid-structure interaction in 3d, Applied Numerical Mathematics 152 (2020), 49-65.
2019
H. Gimperlein, C. Özdemir, D. Stark, E. P. Stephan, hp-version time domain boundary elements for the wave equation on quasiuniform meshes, Computer Methods in Applied Mechanics and Engineering 356 (2019), 145-174.
2018
Führer, Thomas; Heuer, Norbert; Stephan, Ernst P.; On the DPG method for Signorini problems. IMA J. Numer. Anal. 38 (2018), 1893–1926.
Banz, Lothar; Lamichhane, Bishnu P.; Stephan, Ernst P. Higher order FEM for the obstacle problem of the p-Laplacian—a variational inequality approach. Comput. Math. Appl. 76 (2018) 1639–1660.
Banz, Lothar; Lamichhane, Bishnu P.; Stephan, Ernst P. Higher order mixed FEM for the obstacle problem of the p-Laplace equation using biorthogonal systems. Comput. Methods Appl. Math. (2018) (published online).
Stephan, Ernst P.; Teltscher, Matthias T. Collocation with trigonometric polynomials for integral equations to the mixed boundary value problem. Numer. Math. 140 (2018) 153–190.
Gimperlein, Heiko; Meyer, Fabian; Özdemir, Ceyhun; Stark, David; Stephan, Ernst P. Boundary elements with mesh refinements for the wave equation. Numer. Math. 139 (2018) 867–912.
Gwinner, Joachim; Stephan, Ernst Peter Advanced boundary element methods. Treatment of boundary value, transmission and contact problems. Springer Series in Computational Mathematics, 52. Springer, Cham, 2018. xviii+652 pp. ISBN: 978-3-319-92000-9;
Hartmann, Thomas; Stephan, Ernst P. A discrete collocation method for a hypersingular integral equation on curves with corners. Contemporary computational mathematics—a celebration of the 80th birthday of Ian Sloan. Vol. 1, 2, 545–566, Springer, Cham
Gimperlein, Heiko; Meyer, Fabian; Özdemir, Ceyhun; Stephan, Ernst P. Time domain boundary elements for dynamic contact problems. Comput. Methods Appl. Mech. Engrg. 333 (2018), 147–175
Gimperlein, Heiko; Özdemir, Ceyhun; Stephan, Ernst P. Time domain boundary element methods for the Neumann problem: error estimates and acoustic problems. J. Comput. Math. 36 (2018) 70–89.
Ammari, Habib; Bao, Gang; Gatica, Gabriel N.; Nigam, Nilima; Steinbach, Olaf; Stephan, Ernst-Peter; Xu, Liwei; Zhu, Jialin Preface [The 2nd Chongqing Workshop on Computational and Applied Mathematics]. Held at Chongqing University, Chongqing, August 16–19, 2015. J. Comput. Math. 36 (2018), no. 1, i–iv. 65-06
2017
Feischl, Michael;Führer, Thomas;Praetorius, Dirk; Stephan, Ernst P. Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements. Numer. Methods Partial Differential Equations 33 (2017), no. 3, 603–632.
Gimperlein, Heiko; Maischak, Matthias; Stephan, Ernst P. Adaptive time domain boundary element methods with engineering applications. J. Integral Equations Appl. 29 (2017), no. 1,75–105.
Feischl, Michael; Führer, Thomas; Praetorius, Dirk; Stephan, Ernst P. Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations.Calcolo 54 (2017), no. 1, 367–399.
Gimperlein, Heiko; Nezhi, Zouhair; Stephan, Ernst P. A priori error estimates for a time-dependent boundary element method for the acoustic wave equation in a half-space. Math. Methods Appl. Sci. 40 (2017), no. 2, 448–462.
Banz, Lothar; Gimperlein, Heiko; Issaoui, Abderrahman; Stephan, Ernst P.Stabilized mixed hp-BEM for frictional contact problems in linear elasticity. Numer. Math. 135 (2017),no. 1, 217–263.
Banz, Lothar; Lamichhane, Bishnu P.; Stephan, Ernst P. A new three-field formulation of the biharmonic problem and its finite element discretization. Numer. Methods Partial Differential Equations 33 (2017), no. 1, 199–217.
2016
Banz, Lothar; Gimperlein, Heiko; Nezhi, Zouhair; Stephan, Ernst P. Time domain BEM for sound radiation of tires. Comput. Mech. 58 (2016), no. 1, 45–57.
Andres, Michael; Maischak, Matthias; Stephan, Ernst P. Dual-dual formulation for a contact problem with friction. Comput. Methods Appl. Math. 16 (2016), no. 1, 1–16.
Banz, Lothar; Stephan, Ernst P. Comparison of mixed hp-BEM (stabilized and non-stabilized) for frictional contact problems. J. Comput. Appl. Math. 295 (2016), 92–102.
2015
Banz, Lothar; Stephan, Ernst P. On hp-adaptive BEM for frictional contact problems in linear elasticity. Comput. Math. Appl. 69 (2015), no. 7, 559–581.
2014
M. Feischl, T. Führer, G. Mitscha-Eibl, D. Praetorius, E.P. Stephan: Convergence of adaptive BEM and adaptive FEM-BEM coupling for estimators without h-weighting factor. Comput. Methods Appl. Math. 14 (2014), no. 4 485–508
T. von Petersdorff, E.P. Stephan: Decomposition in regular and singular parts (in domains with corners) and stability under perturbation of the geometry. Appl. Anal. 93 (2014), no. 10 2158–2173
A. Costea, H. Gimperlein, E.P. Stephan: A Nash-Hörmander iteration and boundary elements for the Molodensky problem. Numer. Math. 127 (2014), no. 1 1–34
L. Banz, E.P. Stephan: A posteriori error estimates for hp- adaptive IPDG-FEM for elliptic obstacle problems, Applied Numerical Mathematics Volume 76 (2014) 76-92
L. Banz, E.P. Stephan: hp-adaptive IPDG/TDG-FEM for parabolic obstacle problems. Comput. Math. Appl. 67 (2014), no. 4 712–731
M. Maischak, A. Krebs, E.P. Stephan: Quasi-optimal degree distribution for a quadratic programming problem arising from the p-version finite element method for a one-dimensional obstacle problem. Discrete Appl. Math. 164 (2014), part 1, 200–209
L. Banz, A. Costea, H. Gimperlein, E.P. Stephan: Numerical simulationsfor the non-linear Molodensky problem, Stud. Geophys. Geod. 58 (2014) 489-504
H. Gimperlein, Z. Nezhi, E.P. Stephan, A priori error estimates for a time-dependent boundary element method for the acoustic wave equation in a half-space Math.Meth.Appl.Sci (2014) DOI:10.1002/mma.3340
2013
F. Leydecker, M. Maischak, E.P. Stephan, and M. Teltscher: A P-Hierarchical Error Estimator for a FEM-BEM Coupling of an Eddy Current Problem in R^3, J. KSIAM Vol. 17, No.3 (2013) 139-170
B. Denkena, E.P. Stephan et al.: Numerical Computation Methods for Modeling Phenomenon of Tool Extraction, in Process Machine Interactions (ed. B. Denkena, F. Hollmann), Lecture Notes in Production Engineering, Springer 2013, 285-308
M. Andres, E.P. Stephan et al.: Adaptive Finite Elements and Mathematical Optimization Methods,in Process Machine Interactions (ed. B. Denkena, F. Hollmann), Lecture Notes in Production Engineering, Springer 2013, 53-77
L. Banz, E.P. Stephan: hp-adaptive IPDG/TDG FEM for parabolic obstacle problems, Computers a. Mathematics with Appl. (2013), dx.doi.org/10.1016/j.camwa.2013.03.003
A.Costea, H. Gimperlein, and E.P. Stephan: A Nash-Hörmander iteration and boundary elements for the Molodensky problem, Numerische Mathematik (2013), 34 pages, DOI 10.1007/s00211-013-0579-8
L. Banz, A. Costea, H. Gimperlein, and E.P. Stephan: Numerical simulations of the nonlinear Molodensky problem, (proceedings of the European Geosciences Union General Assembly 2013 in Vienna) submitted to Studia geophysica et geodaetica (2013), 13 pages
H. Gimperlein, M. Maischak, and E.P. Stephan: FE-BE Coupling for a Transmission Problem Involving Microstructure, submitted to SIAM Journal on Numerical Analysis (2013), 16 pages
H. Gimperlein, E.P. Stephan: Adaptive FE-BE Coupling for Strongly Nonlinear Transmission Problems with Friction II, submitted to SIAM Journal on Numerical Analysis (2013), 20 pages
E.P. Stephan et al.: High precision modeling towards the 10-20 level, ZAMM, Z. Angew. Math. Mech. 93 (2013) 492-498
R. Bürger, O Steinbach, and E.P. Stephan: Editorial Special Issue: PDE's: Theory, application simulations, ZAMM, Z. Angew. Math. Mech. 93 (2013)
2012
C. Dominguez Garcia,E.P. Stephan, and M. Maischak: A FE-BE coupling for a fluid-structure interaction problem: hierarchical a posteriori error estimates. Numer. Methods Partial Differential Equations 28 (2012), 1417-1439
B.P. Lamichhane, E.P. Stephan: A symmetric mixed finite element method for nearly incompressible elasticity based on biorthogonal systems. Numer. Methods Partial Differential Equations 28 (2012), 1336-1353
M. Gläfke, M. Maischak, and E.P Stephan: Coupling of FEM and BEM for a transmission problem with nonlinear interface conditions. Hierarchical and residual error indicators. Appl. Numer. Math. 62 (2012), 736-753
M. Maischak, S. Oestmann, E.P. Stephan: A least-squares fem-bem coupling method for linear elasticity. Appl. Numer. Math. 62 (2012) 457-472
M. Andres, M. Maischak, and E.P. Stephan: Dual-dual formulation for a contact problem with friction. Numer. Math. (submitted)
L. Nesemann, E.P. Stephan: Numerical solution of an adhesion problem with FEM and BEM. Appl. Numer. Math 62 (2012) 606-619
C. Dominquez Garcia, E.P. Stephan, M. Maischak: A FE/BE coupling for an acoustic fluid-structure interaction problem. Residual a posteriori error estimates. Int. J. Numer. Methods Eng. 89 (2012) 299-322
B. Lamichhane, E.P. Stephan: A symmetric mixed finite element method for nearly incompressible elasticity based on biorthogonal systems. Numer. Methods Partial Differ. Equations, 28 (2012) 1336-1353
F. Leydecker, E.P. Stephan: Additive Schwarz methods for the hp-version of the boundary element method in R^3. in: Fast BEM in Engeneering and Industrial Applications (editors: U. Langer, O. Steinbach) Lecture notes Applied and Computational Mechanics 63, Springer (2012)
F. Leydecker, M. Maischak, E.P. Stephan, and M. Teltscher: A p-hierarchical error estimator for a FE-BE coupling formulation applied to electromagnetic scattering problems in R^3. Appl. Anal. 91 (2012) 277-293
2011
G.N. Gatica, M. Maischak, and E.P. Stephan: Numerical Analysis of a Transmission Problem with Signorini Contact using mixed-FEM and BE, ESAIM Math. Model. Numer. Anal. 45 (2011) 779-802
H. Gimperlein, M. Maischak, E. Schrohe, and E.P. Stephan: Adaptive FE-BE coupling for strongly nonlinear transmission problems with Coulomb friction. Numer. Math. 117 (2011) 307-332
M. Andres, H. Blum, C. Brandt, C. Carstensen, P. Maass , J. Niebsch, A., Rademacher, R. Ramlau, A. Schröder, E.P. Stephan, and S. Wiedemann: Adaptive finite elements and mathematical optimization methods. Springer Book: Process Machine Interactions (to be published)
Q.T Le Gia, E.P. Stephan, and T. Tran: Solution to the Neumann problem exterior to a prolate spheroid by radial basis functions, Adv. Comput. Math. 34 (2011) 83-103
2010
E.P. Stephan, W.L. Wendland, G.C. Hsiao on his 75th birthday Math Methods Appl. Sci. 33 (2010) 2143-2144
A. Costea, Q.T. Le Gia, E.P. Stephan, and T. Tran: Meshless BEM and overlapping Schwarz preconditioners for exterior problems on spheroids, Studia Geophysica et Geodetica, vol. 55, iss. 3
M. Maischak, A. Krebs, and E.P. Stephan: A quadratic programming problem arising from the p-version for obstacle problems, Electronic Notes in Discrete Mathematics 36 923-930
E.P. Stephan, A. Costea, Q.T. Le Gia, and T. Tran: Meshless boundary element methods for exterior problems on spheroids, Advances in Boundary Element Techniques XI, conference proceedings, International Conference on Boundary Element and Meshless Techniques 455-462
B. Denkena, D. Heinisch, M. Krüger, E.P. Stephan, M. Maischak, and M. Andres: investigations on Dynamic Tool, Structure and Process Interaction, Proceedings of the 2nd International Conference Process Machine Interactions (PMI)
E.P. Stephan, S. Geyn, and M. Maischak: Coupling of Boundary Elements and Finite Elements in Incremental Forming. Final report of the DFG priority program SPP 1146, Modelling of incremental forming processes, Shaker Verlag, Aachen 69-74
F. Leydecker, M. Maischak, E.P. Stephan, M. Teltscher: Adaptive FE-BE coupling for an electromagnetic problem in R3-a residual error estimator, Math. Methods Appl. Sci. 33 (2010) 162-2186
A. Krebs, M. Maischak, E.P. Stephan: Adaptive FEM BEM coupling with a Schur complement error indicator, Appl. Numer. Math. 60 (2010) 798-808
R. Prato Torres, E.P. Stephan, F. Leydecker: A FE/BE coupling for the 3D time-dependent eddy current problem. Part II: a posteriori error estimates and adaptive computations,, Computing 88 (2010) 155-172
R. Prato Torres, E.P. Stephan, F. Leydecker: A FE/BE coupling for the 3D time-dependent eddy current problem. Part I: a priori error estimates,, Computing 88 (2010) 31-154
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) 141-163
2009
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)2857-2871
M. Maischak, E. Ostermann, E. P. Stephan: TD-BEM forSound Radiation in three Dimensions and the Numerical Evaluation of Retarded Potentials, NAG/DAGA 2009 - Rotterdam (2009) 633-636
E. P. Stephan: The hp-Version of BEM - Fast Convergence, Adaptivity and Efficient Preconditioning, Journal of Computational Mathematics, 27 (2009) 348-359
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
E. P. Stephan, T. Tran, A. Costea: A boundary integralequation on the sphere for high-precision geodesy. Computer Methods in Mechanics - Lecture Notes on the CMM 2009, edited by Kuczma, Wilmanski, (2009)
2008
E.P. Stephan: Efficient Coupling of Finite Elements and Boundary Elements - Adaptive Procedures and Preconditioning, ANZIAM J. 50 (2008) C774-C799
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
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 (2008) 321-330
F.-D. Speck, E.P. Stephan: Boundary value problems for the Helmholtz equation in an octant, Integral Eqn. Oper. Theory, 62 (2008) 269-300
H. Holm, M. Maischak, E. P. Stephan: Math. Meth. Appl. Sci., 31 (2008) 2069-2093
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) 2029-2054
2007
M. Maischak, E.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
A. Chernov, E.P. Stephan: Adaptive BEM for Contact Problems with Friction, Proceedings of the IUTAM (2007) 113-122
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) 3871-3880
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)3348-3369
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
Krebs, Andreas; Stephan, Ernst P.: p-version finite element method for nonlinear elliptic variational inequalities in 2D. Numer. Math. 105 (2007) 457-480
M. Maischak, E.P. Stephan: Adaptive hp-versions of boundary element methods for elastic contact problems Comput. Mech. 39 (2007) 597-607
E.P. Stephan, M. Maischak, F. Leydecker: An hp-adaptive finite element/boundary element coupling method for electromagnetic problems, Comput. Mech. 39 (2007) 673-680
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
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
E.P. Stephan, M. Maischak, F. Leydecker: Some Schwarz methods for integral equations on surfaces- h and p versions,Comput. Vis. Sci. 8 (2005) 211-216.
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) 1119-1139
M. Maischak, E.P. Stephan: Adaptive hp-versions of BEM for Signorini problems, Appl. Numer. Math. 54 (2005) 425-449
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) 427-439
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) 441-452
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) 453-466
