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Heinrich, Bernd; Jung, Beate : Nitsche finite element method

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