Document Free access article
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 Wagner31 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