A FETI-DP preconditioner with a special scaling for mortar discretization of elliptic problems with discontinuous coefficients

We consider two-dimensional elliptic problems with discontinuous coefficients discretized by the finite element method on geometrically conforming nonmatching triangulations across the interface using the mortar technique. The resulting discrete problem is solved by a dual-primal FETI method. In this paper we introduce and analyze a preconditioner with a special scaling of coefficients and step parameters and establish convergence bounds. We show that the preconditioner is almost optimal with constants independent of the jumps of coefficients and step parameters. Extensive computational evidence is presented that illustrates an almost optimal convergence for a variety of situations (distribution of subregions, grid assignment, grid ratios, number of subregions) for both continuous and discontinuous problems.