A Nitsche finite element approach for elliptic problems with discontinuous Dirichlet boundary conditions
Publisher DOI
Abstract
We present a numerical approximation method for linear elliptic diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known singular functions as well as of an H²-regular part. The latter part is expressed in terms of an elliptic problem with regularized Dirichlet boundary conditions, and can be approximated by means of a Nitsche finite element approach. The discrete solution of the original problem is then defined by adding back the singular part of the exact solution to the Nitsche approximation. In this way, the discrete solution can be shown to converge of second order in the L²-norm with respect to the mesh size.
Date Issued
2018
Publication Type
Article
Subject(s)
Language(s)
en
Additional Credits
Journal
Computational methods in applied mathematics
Publisher
De Gruyter
ISSN
1609-4840
Access(Rights)
open.access