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A Multigrid Algorithm For The Mortar Finite Element Method (0)
| Venue: | SIAM J. Numer. Anal |
| Citations: | 57 - 10 self |
BibTeX
@ARTICLE{Braess_amultigrid,
author = {Dietrich Braess and Wolfgang Dahmen and CHRISTIAN WIENERS},
title = {A Multigrid Algorithm For The Mortar Finite Element Method},
journal = {SIAM J. Numer. Anal},
year = {},
volume = {37},
pages = {48--69}
}
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Abstract
The objective of this paper is to develop and analyse a multigrid algorithm for the system of equations arising from the mortar finite element discretization of second order elliptic boundary value problems. In order to establish the inf-sup condition for the saddle point formulation and to motivate the subsequent treatment of the discretizations we revisit first briefly the theoretical concept of the mortar finite element method. Employing suitable mesh-dependent norms we verify the validity of the LBB condition for the resulting mixed method and prove an L 2 error estimate. This is the key for establishing a suitable approximation property for our multigrid convergence proof via a duality argument. In fact, we are able to verify optimal multigrid efficiency based on a smoother which is applied to the whole coupled system of equations. We conclude with several numerical tests of the proposed scheme which confirm the theoretical results and show the efficiency and the robustness of t...
Keyphrases
mortar finite element method multigrid algorithm saddle point formulation optimal multigrid efficiency multigrid convergence proof lbb condition mixed method inf-sup condition first briefly subsequent treatment suitable mesh-dependent norm suitable approximation property theoretical result mortar finite element discretization theoretical concept several numerical test error estimate duality argument
