Geodesic
Finite Element Method with Patches for Poisson problems in polygonal domains
Alexei Lozinski1 ; Jacques Rappaz2 ; Joël Wagner3
1 Dept. of Mathematics, University of Houston, 4800 Calhoun Road, Houston, Texas 77204-3008, USA (
2 Section of Mathematics, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland ().
3 .
ESAIM. Proceedings, Tome 21 (2007), pp. 45-64.

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In this paper we consider the finite element approximation of the singularities of the solution of Poisson problems in a polygonal domain with reentrant corners or changing Dirichlet-Neumann boundary conditions. We use a correction algorithm with patches of elements to improve the a priori error estimates and to obtain the same order as the optimal estimate when everything is regular. We give an application of the correction method to the problem of glacier modeling.
DOI : 10.1051/proc:072105

Alexei Lozinski 1 ; Jacques Rappaz 2 ; Joël Wagner 3

1 Dept. of Mathematics, University of Houston, 4800 Calhoun Road, Houston, Texas 77204-3008, USA (
2 Section of Mathematics, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland ().
3 . 
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     title = {Finite {Element} {Method} with {Patches} for {Poisson} problems in polygonal domains},
     journal = {ESAIM. Proceedings},
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Alexei Lozinski; Jacques Rappaz; Joël Wagner. Finite Element Method with Patches for Poisson problems in polygonal domains. ESAIM. Proceedings, Tome 21 (2007), pp. 45-64. doi : 10.1051/proc:072105. http://geodesic.mathdoc.fr/articles/10.1051/proc:072105/

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