On optimal L2- and surface flux convergence in FEM

T. Horger; J. M. Melenk; B. Wohlmuth

doi:10.1007/s00791-015-0237-z

On optimal L²- and surface flux convergence in FEM

T. Horger, J. M. Melenk, B. Wohlmuth

Chair of Numerical Analysis

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10 Scopus citations

Abstract

We show that optimal the boundary value problem has the mapping property (Formula present)for (Formula present). The lack of full elliptic regularity in the dual problem has to be compensated by additional regularity of the exact solution. Furthermore, we analyze for a Dirichlet problem the approximation of the normal derivative on the boundary without convexity assumption on the domain. We show that (up to logarithmic factors) the optimal rate is obtained.

Original language	English
Pages (from-to)	231-246
Number of pages	16
Journal	Computing and Visualization in Science
Volume	16
Issue number	5
DOIs	https://doi.org/10.1007/s00791-015-0237-z
State	Published - Oct 2013

Keywords

Duality argument
L a priori bounds
Reentrant corners

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AU - Wohlmuth, B.

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N2 - We show that optimal the boundary value problem has the mapping property (Formula present)for (Formula present). The lack of full elliptic regularity in the dual problem has to be compensated by additional regularity of the exact solution. Furthermore, we analyze for a Dirichlet problem the approximation of the normal derivative on the boundary without convexity assumption on the domain. We show that (up to logarithmic factors) the optimal rate is obtained.

AB - We show that optimal the boundary value problem has the mapping property (Formula present)for (Formula present). The lack of full elliptic regularity in the dual problem has to be compensated by additional regularity of the exact solution. Furthermore, we analyze for a Dirichlet problem the approximation of the normal derivative on the boundary without convexity assumption on the domain. We show that (up to logarithmic factors) the optimal rate is obtained.

KW - Duality argument

KW - L a priori bounds

KW - Reentrant corners

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ER -

On optimal L²- and surface flux convergence in FEM

Abstract

Keywords

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