Paper Info
Title
A Multigrid Algorithm for the Mortar Finite Element Method
Abstract
The objective of this paper is to develop and analyze 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 first revisit briefly the theoretical concept of the mortar finite element method. Employing suitable mesh-dependent norms we verify the validity of the Ladyzhenskaya--Babuska--Brezzi (LBB) condition for the resulting mixed method and prove an L2 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 the method even in situations not covered by the theory.
Year
DOI
Venue
1999
10.1137/S0036142998335431
SIAM J. Numerical Analysis
Keywords
Field
DocType
optimal multigrid efficiency,multigrid algorithm,mortar finite element method,order elliptic boundary value,suitable approximation property,mixed method,mortar finite element discretization,inf-sup condition,suitable mesh-dependent norm,multigrid convergence proof,second order,saddle point,system of equations,domain decomposition
Boundary value problem,Discretization,Mathematical optimization,Saddle point,System of linear equations,Mathematical analysis,Bramble–Hilbert lemma,Finite element method,Mathematics,Multigrid method,Domain decomposition methods
Journal
Volume
Issue
ISSN
37
1
0036-1429
Citations 
PageRank 
References 
32
8.02
1
Authors
3
Name
Order
Citations
PageRank
Dietrich Braess122528.90
Wolfgang Dahmen2328.02
christian wieners38417.69