Adaptive T-spline discretization for nonlinear partial differential equations (PDEs)
This presentation introduces adaptive T-spline discretization for nonlinear partial differential equations (PDEs) within the isogemetric analysis (IGA) framework of “deal.t”, an extension of “deal.II”. By exploiting T-splines ability to curved parametrize curved boundaries exactly - eliminating discretizations errors - we address challenges in solving nonlinear problems like the minimal surface equation and a cubic nonlinear Poisson equation. This talk will contrast the IGA-based approach with the classical finite element method (FEM). After a short mathematical introduction it demonstrates convergence rates and robustness of the method by means of numerical benchmarks.
