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Universität Stuttgart Mortar Finite Elements for Interface Problems

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 the saddle point formulation and show that the interface conditions enter in 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.