Frequency filtering for elliptic interface problems with Lagrange multipliers

The solution of the saddle point interface problem arising in hybrid formulation with the Lagrange multipliers for elliptic problems with nonmatching grids is considered. The preconditioner is constructed using frequency filtering decompositions of the local Schur complements. The convergence rate of the resulting iterative process does not depend on the size of the interface problem. The approach is applied for the treatment of the local refinement procedures and considered as an alternative to the refinement with slave nodes or full closure of the grid. Numerical experiments on the convergence rate are presented.