Geodesic
A multilevel preconditioner for the mortar method for nonconforming P 1 finite element
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 3, pp. 429-444

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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.

DOI : 10.1051/m2an/2009003
Classification : 65F10, 65N30, 65N55
Keywords: Crouzeix-Raviart FE, mortar method, multilevel preconditioner, auxiliary space method 
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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 },
     pages = {429--444},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {3},
     year = {2009},
     doi = {10.1051/m2an/2009003},
     mrnumber = {2527400},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2009003/}
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Rahman, Talal; Xu, Xuejun. A multilevel preconditioner for the mortar method for nonconforming $P_1$ finite element. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 3, pp. 429-444. doi: 10.1051/m2an/2009003

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