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Zbl 1024.65111
Wohlmuth, Barbara I.
A comparison of dual Lagrange multiplier spaces for mortar finite element discretizations. (English)
[J] M2AN, Math. Model. Numer. Anal. 36, No.6, 995-1012 (2002). ISSN 0764-583X; ISSN 1290-3841/e

Summary: Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We focus on mortar finite element methods on non-matching triangulations. In particular, we discuss and analyze dual Lagrange multiplier spaces for lowest order finite elements. These non standard Lagrange multiplier spaces yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces. \par As a consequence, standard efficient iterative solvers as multigrid methods or domain decomposition techniques can be easily adapted to the nonconforming situation. Here, we introduce new dual Lagrange multiplier spaces. We concentrate on the construction of locally supported and continuous dual basis functions. The optimality of the associated mortar method is shown. Numerical results illustrate the performance of our approach.

MSC 2000:: *65N30 Finite numerical methods (BVP of PDE)
65N55 Multigrid methods; domain decomposition (BVP of PDE)
35J25 Second order elliptic equations, boundary value problems

Keywords: mortar finite elements; second-order elliptic boundary value problem; non-matching triangulations; multigrid methods; domain decomposition; dual Lagrange multiplier spaces; numerical results

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