Repository: Freie Universit├Ąt Berlin, Math Department

A multigrid method based on the unconstrained product space for Mortar finite element discretizations

Wohlmuth, B. and Krause, R. (2001) A multigrid method based on the unconstrained product space for Mortar finite element discretizations. SIAM Journal on Numerical Analysis, 39 (1). pp. 192-213. ISSN 0036-1429

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Official URL: https://dx.doi.org/10.1137/S0036142999360676

Abstract

The mortar finite element method allows the coupling of different discretizations across subregion boundaries. In the original mortar approach, the Lagrange multiplier space enforcing a weak continuity condition at the interfaces is defined as a modified finite element trace space. Here we present a new approach, where the Lagrange multiplier space is replaced by a dual space without losing the optimality of the a priori bounds. We introduce new dual spaces in 2D and 3D. Using the biorthogonality between the nodal basis functions of this Lagrange multiplier space and a finite element trace space, we derive an equivalent symmetric positive definite variational problem defined on the unconstrained product space. The introduction of this formulation is based on a local elimination process for the Lagrange multiplier. This equivalent approach is the starting point for the efficient iterative solution by a multigrid method. To obtain level independent convergence rates for the $\Cw$-cycle, we have to define suitable level dependent bilinear forms and transfer operators. Numerical results illustrate the performance of our multigrid method in 2D and 3D.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Numerical Analysis
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:1847
Deposited By: Ekaterina Engel
Deposited On:06 Mar 2016 16:22
Last Modified:18 Apr 2016 19:13

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