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

Full text not available from this repository.

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 |
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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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