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- W2081305152 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." @default.
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- W2081305152 date "2001-01-01" @default.
- W2081305152 modified "2023-09-24" @default.
- W2081305152 title "A Multigrid Method Based on the Unconstrained Product Space for Mortar Finite Element Discretizations" @default.
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- W2081305152 doi "https://doi.org/10.1137/s0036142999360676" @default.
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