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A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D

Published online by Cambridge University Press:  15 February 2004

Bishnu P. Lamichhane
Affiliation:
Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Germany. lamichhane@mathematik.uni-stuttgart.de.;wohlmuth@mathematik.uni-stuttgart.de.
Barbara I. Wohlmuth
Affiliation:
Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Germany. lamichhane@mathematik.uni-stuttgart.de.;wohlmuth@mathematik.uni-stuttgart.de.
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Abstract

Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces in case of hexahedral triangulations. As a result, standard efficient iterative solvers as multigrid methods can be easily adapted to the nonconforming situation. We present the discretization errors in different norms for linear and quadratic mortar finite elements with different Lagrange multiplier spaces. Numerical results illustrate the performance of our approach.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2004

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