A multilevel preconditioner for the mortar method for nonconforming P 1 finite element
Rahman, Talal ; Xu, Xuejun
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009), p. 429-444 / Harvested from Numdam
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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.

Publié le : 2009-01-01
DOI : https://doi.org/10.1051/m2an/2009003
Classification:  65F10,  65N30,  65N55 
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     author = {Rahman, Talal and Xu, Xuejun},
     title = {A multilevel preconditioner for the mortar method for nonconforming $P\_1$ finite element},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {43},
     year = {2009},
     pages = {429-444},
     doi = {10.1051/m2an/2009003},
     mrnumber = {2527400},
     zbl = {pre05574326},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2009__43_3_429_0}
}

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) pp. 429-444. doi : 10.1051/m2an/2009003. http://gdmltest.u-ga.fr/item/M2AN_2009__43_3_429_0/

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