Name
Title | ||
|---|---|---|
A Multigrid Method Based on the Unconstrained Product Space for Mortar Finite Element Discretizations |
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. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1137/S0036142999360676 | SIAM Journal on Numerical Analysis |
Keywords | Field | DocType |
mortar finite elements,Lagrange multiplier,dual space,nonmatching triangulations,multigrid methods,level dependent bilinear forms | Bilinear form,Mathematical analysis,Lagrange multiplier,Dual space,Finite element method,Basis function,Numerical analysis,Multigrid method,Mathematics,Mixed finite element method | Journal |
Volume | Issue | ISSN |
39 | 1 | 0036-1429 |
Citations | PageRank | References |
6 | 1.24 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Barbara I. Wohlmuth | 1 | 320 | 50.97 |
| Rolf H. Krause | 2 | 23 | 4.83 |