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A Comparison of Dual Lagrange Multiplier Spaces for Mortar Finite Element Discretizations

Published online by Cambridge University Press:  15 January 2003

Barbara I. Wohlmuth
Barbara I. Wohlmuth*
Affiliation:
Math. Institut, Universität Stuttgart, Pfaffenwaldring 57, 70 569 Stuttgart, Germany. wohlmuth@mathematik.uni-stuttgart.de.
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Abstract

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 spacesfor lowest order finite elements.These non standard Lagrange multiplier spaces yield optimal discretizationschemes and a locally supported basis for the associatedconstrained mortar spaces. As a consequence,standard efficient iterative solvers as multigrid methods or domain decomposition techniques can be easily adapted to the nonconformingsituation.Here, we introduce new dual Lagrange multiplier spaces. We concentrateon the construction of locally supported and continuous dualbasis functions.The optimality of the associated mortar method is shown. Numerical results illustrate the performance of our approach.

Keywords

Mortar finite elementsdual spacenon-matching triangulationsmultigrid methods.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 6 , November 2002 , pp. 995 - 1012
Copyright
© EDP Sciences, SMAI, 2002

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