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Issue ESAIM: Proc.
Volume 21, 2007
Journées d'analyse fonctionnelle et numérique en l'honneur de Michel Crouzeix
Page(s) 45 - 64
DOI http://dx.doi.org/10.1051/proc:072105
Published online 04 December 2007

ESAIM: Proc., 2007, Vol. 21, pp. 45-64
DOI: 10.1051/proc:072105

Finite Element Method with Patches for Poisson problems in polygonal domains

Alexei Lozinski1, Jacques Rappaz2 and 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  .


(Published online: 4 December 2007)

Abstract
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.


Mathematics Subject Classification. 65N55, 65N30, 65N15

Key words: a priori error estimate, multiplicative Schwarz algorithm, singularities of the solution of Poisson problems, glacier modeling


© EDP Sciences, ESAIM 2007


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