Domain decomposition methods on nonmatching grids and some applications to linear elasticity problems

Abstract

Domain decomposition techniques provide a powerful tool for the coupling of different discretization methods or nonmatching triangulations across subregion boundaries. Here, we consider mortar finite elements methods for linear elasticity and diffusion problems. These domain decomposition techniques provide a more flesible approach than standard conforming formulations. The mortar solution is weakly continuous at subregion boundaries, and its jump is orthogonal to a suitable Lagrange multiplier space. Our approach is based on dual bases for the Lagrange true for the standard mortar method [2]. The biorthogonality relation guarantees that the Lagrange multiplier can be locally eliminated, and that we obtain a symmetric positive semidefinite system on the unconstrained product space. This system will be solved by multigrid techniques. Numerical results illustrate the performance of the multigrid method in 2D and 3D.