Heinrich, Bernd ; Jung, Beate : Nitsche finite element method
- Author(s):
-
Heinrich, Bernd
Jung, Beate
- Title:
- Nitsche finite element method
- Electronic source:
-
application/pdf
- Preprint series:
- Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 23, 2007
- Mathematics Subject Classification:
-
65M60 [ Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods ] 65N30 [ Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods ] - Abstract:
- This paper deals with a method for the numerical solution of parabolic initial-boundary value problems in two-dimensional polygonal domains~$\Omega$ which are allowed to be non-convex. The Nitsche finite element method (as a mortar method) is applied for the discretization in space, i.e. non-matching meshes are used. For the discretization in time, the backward Euler method is employed. The rate of convergence in some $H^1$-like norm and in the $L_2$-norm is proved for the semi-discrete as well as for the fully discrete problem. In order to improve the accuracy of the method in presence of singularities arising in case of non-convex domains, meshes with local grading near the reentrant corner are employed for the Nitsche finite element method. Numerical results illustrate the approach and confirm the theoretically expected convergence rates.
- Keywords:
- parabolic problem, corner singularity, semidiscrete finite element method, non-matching meshes, Nitsche mortaring, fully discrete method
- Language:
-
English
- Publication time:
- 11 / 2007
