A posteriori error estimations of a coupled mixed and standard Galerkin method

pages

English

Documents

Lire un extrait

Obtenez un accès à la bibliothèque pour le consulter en ligne En savoir plus

Découvre YouScribe en t'inscrivant gratuitement

Je m'inscris

Découvre YouScribe en t'inscrivant gratuitement

Je m'inscris

pages

English

Ebook

Lire un extrait

Obtenez un accès à la bibliothèque pour le consulter en ligne En savoir plus

Publié par

profil-vieg-2012

Nombre de lectures

Langue

English

Niveau: Supérieur, Licence, Bac+2
A posteriori error estimations of a coupled mixed and standard Galerkin method for second order operators Emmanuel Creuse, Serge Nicaise Universite de Valenciennes et du Hainaut Cambresis LAMAV Institut des Sciences et Techniques de Valenciennes F-59313 - Valenciennes Cedex 9 France Emmanuel.Creuse, June 14, 2006 Abstract In this paper, we consider a discretization method proposed by Wieners and Wohlmuth [26] (see also [16]) for second order operators, which is a coupling between a mixed method in a sub-domain and a standard Galerkin method in the remaining part of the domain. We perform an a posteriori error analysis of residual type of this method, by combining some arguments from a posteriori error analysis of Galerkin methods and mixed methods. The reliability and efficiency of the estimator are proved. Some numerical tests are presented and confirm the theoretical error bounds. 1 Introduction Let us fix a bounded domain ? of R2, with a polygonal boundary. For the sake of simplicity we assume that ? is simply connected. The case of a multiply connected domain can be treated as in [12]. In this paper we consider the following second order problem: For f ? L2(?), let ? ? H10 (?) be the unique solution of div (A??) = ?f in ?, (1) where the matrix A ? L∞(?,R2?2) is supposed to be symmetric and uniformly positive definite.

div ? ?

priori error

crouzeix-raviart property

included into

all elements

universite de valenciennes et du hainaut cambresis

include standard

standard galerkin

Voir

Publié par

profil-vieg-2012

Nombre de lectures

Langue

English

Créuse Saint Nicaise

A posteriori error estimations coupled mixed and standard Galerkin for second order operators

EmmanuelCreus´e,SergeNicaise

method

Universite´deValenciennesetduHainautCambre´sis

LAMAV Institut des Sciences et Techniques de Valenciennes F-59313 - Valenciennes Cedex 9 France Emmanuel.Creuse,Serge.Nicaise@univ-valenciennes.fr

June 14, 2006

Abstract

In this paper, we consider a discretization method proposed by Wieners and Wohlmuth [26] (see also [16]) for second order operators, which is a coupling between a mixed method in a sub-domain and a standard Galerkin method in the remaining part of the domain. We perform an a posteriori error analysis of residual type of this method, by combining some arguments from a posteriori error analysis of Galerkin methods and mixed methods. The reliability and eﬃciency of the estimator are proved. Some numerical tests are presented and conﬁrm the theoretical error bounds.

1 Introduction Let us ﬁx a bounded domain Ω ofR2 For the sake of simplicity, with a polygonal boundary. we assume that Ω is simply connected. The case of a multiply connected domain can be treated as in [12]. In this paper we consider the following second order problem: Forf∈L2(Ω), let θ∈H1(Ω) be the unique solution of 0