Issue ESAIM: M2AN Volume 43, Number 3, May-June 2009 Page(s) 429 - 444 DOI 10.1051/m2an/2009003 Published online 07 February 2009

ESAIM: M2AN 43 (2009) 429-444
DOI: 10.1051/m2an/2009003

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

Talal Rahman^{1, 2} and Xuejun Xu<sup>3

1</sup>  Department of Mathematics, University of Bergen, c/o Center for Integrated Petroleum Research, Allegt. 41, 5007 Bergen, Norway. talal.rahman@math.uib.no
²  Present address: Faculty of Engineering, Bergen University College, 5020 Bergen, Norway.
³  LSEC, Institute of Computational Mathematics, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, P.R. China. xxj@lsec.cc.ac.cn

Received April 3rd, 2007. Published online February 7, 2009.

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.

Mathematics Subject Classification. 65F10, 65N30, 65N55

Key words: Crouzeix-Raviart FE, mortar method, multilevel preconditioner, auxiliary space method.


© EDP Sciences, SMAI 2009

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