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A multilevel preconditioner for the mortar method for nonconforming P1 finite element

Published online by Cambridge University Press:  07 February 2009

Talal Rahman  and
Xuejun Xu
Talal Rahman
Affiliation:
Department of Mathematics, University of Bergen, c/o Center for Integrated Petroleum Research, Allegt. 41, 5007 Bergen, Norway. talal.rahman@math.uib.no Present address: Faculty of Engineering, Bergen University College, 5020 Bergen, Norway.
Xuejun Xu
Affiliation:
LSEC, Institute of Computational Mathematics, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, P.R. China. xxj@lsec.cc.ac.cn
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Abstract

A multilevel preconditioner based on the abstract framework of the auxiliary space method, is developed for the mortar method for the nonconforming P1 finite element or the lowest order Crouzeix-Raviart finite element on nonmatching grids. It is shown that the proposed preconditioner is quasi-optimal in the sense that the condition number of the preconditioned system is independent of the mesh size, and depends only quadratically on the number of refinement levels. Some numerical results confirming the theory are also provided.

Keywords

Crouzeix-Raviart FEmortar methodmultilevel preconditionerauxiliary space method.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 3 , May 2009 , pp. 429 - 444
Copyright
© EDP Sciences, SMAI, 2009

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