A posteriori error estimates and domain decomposition with nonmatching grids
type: Item
instance of: scholarly article
title: A posteriori error estimates and domain decomposition with nonmatching grids
zbMATH Open document ID: 1071.65144
author: J. Pousin
author: Taoufik Sassi
published in: Advances in Computational Mathematics
publication date: 2005-05-20T00:00:00Z
review text: The purpose is to extend the adapive mortar finite element techniques to a nonlinear boundary value problem and to prove that the corresponding residual estimator is asymptotically equivalent to the so-called Babuška-Rheinboldt error estimator [see \textit{I. Babuška} and \textit{W. C. Rheinboldt}, Int. J. Numer. Methods Eng. 12, 1597--1615 (1978; Zbl 0396.65068) and SIAM J. Numer. Anal. 15, 736--754 (1978; Zbl 0398.65069)]. The Petrov-Galerkin finite element method is combined with a domain decomposition method with nonmatching grid. Then the residual estimator for a model semi-linear problem is proposed. The given problem is equivalent formulated to a saddle-point problem which is approximated by a finite element method, in particular, the mortar finite element technique is considered. This mortar method is characterized by introducing a discrete Lagrange multiplier space by a suitable triangulation. For the solution of the saddle-point problem Theorem 1 gives three error estimates. In Section 4, an error estimator for a model problem by a particular choice of the saddle-point problem is discussed. Two numerical results are presented.
reviewed by: Iulian Coroian
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N55
zbMATH DE Number: 2170075
zbMATH Keywords: nonlinear elliptic problem
zbMATH Keywords: a posteriori error estimates
zbMATH Keywords: mortar finite element method
zbMATH Keywords: domain decomposition methods
zbMATH Keywords: nonlinear boundary value problem
zbMATH Keywords: saddle-point problem
zbMATH Keywords: numerical results
MaRDI profile type: Publication
full work available at URL: s10444-004-1779-7
OpenAlex ID: W2068980215
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DOI: 10.1007/S10444-004-1779-7
description: scientific article; zbMATH DE number 2170075