Rahman, Talal; Xu, Xuejun
A multilevel preconditioner for the mortar method for nonconforming P 1 finite element
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009) no. 3 , p. 429-444
Zbl pre05574326 | MR 2527400
doi : 10.1051/m2an/2009003
URL stable : http://www.numdam.org/item?id=M2AN_2009__43_3_429_0

Classification:  65F10,  65N30,  65N55
A multilevel preconditioner based on the abstract framework of the auxiliary space method, is developed for the mortar method for the nonconforming P 1 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.

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