Abstract
Mortar techniques provide a flexible tool for the coupling of different discretization schemes or triangulations. Here, we consider interface problems within the framework of mortar finite element methods. We start with a saddle point formulation and show that the interface conditions enter into the right-hand side. Using dual Lagrange multipliers, we can work with scaled sparse matrices, and static condensation gives rise to a symmetric and positive definite system on the unconstrained product space. The iterative solver is based on a modified multigrid approach. Numerical results illustrate the performance of our approach.
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This work was supported in part by the Deutsche Forschungsgemeinschaft, SFB 404, C12.
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Lamichhane, B., Wohlmuth, B. Mortar Finite Elements for Interface Problems. Computing 72, 333–348 (2004). https://doi.org/10.1007/s00607-003-0062-y
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DOI: https://doi.org/10.1007/s00607-003-0062-y
Keywords
- Mortar finite elements
- Lagrange multiplier
- saddle point problem
- domain decomposition
- interface problem
- non-matching triangulation