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

Talal Rahman; Xuejun Xu

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 3, page 429-444
  • ISSN: 0764-583X

Abstract

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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 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.

How to cite

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Rahman, Talal, and Xu, Xuejun. "A multilevel preconditioner for the mortar method for nonconforming P1 finite element." ESAIM: Mathematical Modelling and Numerical Analysis 43.3 (2009): 429-444. <http://eudml.org/doc/250637>.

@article{Rahman2009,
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. },
author = {Rahman, Talal, Xu, Xuejun},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Crouzeix-Raviart FE; mortar method; multilevel preconditioner; auxiliary space method.; nonconforming elements; Crouzeix-Raviart elements},
language = {eng},
month = {2},
number = {3},
pages = {429-444},
publisher = {EDP Sciences},
title = {A multilevel preconditioner for the mortar method for nonconforming P1 finite element},
url = {http://eudml.org/doc/250637},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Rahman, Talal
AU - Xu, Xuejun
TI - A multilevel preconditioner for the mortar method for nonconforming P1 finite element
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2009/2//
PB - EDP Sciences
VL - 43
IS - 3
SP - 429
EP - 444
AB - 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.
LA - eng
KW - Crouzeix-Raviart FE; mortar method; multilevel preconditioner; auxiliary space method.; nonconforming elements; Crouzeix-Raviart elements
UR - http://eudml.org/doc/250637
ER -

References

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