Original article

Numerische Mathematik

, Volume 84, Issue 2, pp 173-197

First online:

The Mortar finite element method with Lagrange multipliers

  • Faker Ben BelgacemAffiliated withLaboratoire de Mathématiques pour l'Industrie et la Physique, Unité Mixte de Recherche CNRS–UPS–INSAT–UT1 (UMR 5640), Université Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex 04, France

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The present paper deals with a variant of a non conforming domain decomposition technique: the mortar finite element method. In the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices (and the edges in 3D) of subdomains. It is shown that, written under primal hybrid formulation, the approximation problem, issued from a discretization of a second order elliptic equation in 2D, is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms. Finally the parallelization advantages consequence of this variant are also addressed.

Mathematics Subject Classification (1991):65N30