FETI-DP method for DG discretization of elliptic problems with discontinuous coefficients

In the talk a discontinuous Galerkin (DG) approximation of elliptic problems with discontinuous coefficients will be discussed. The problem is considered in polygonal region $\mathrm{\Omega }$ which is a union of disjoint polygonal subregions ${\mathrm{\Omega }}_i$. The discontinuities of the coefficients occur across $\partial {\mathrm{\Omega }}_i$. The problem is approximated by a conforming finite element method (FEM) on matching triangulation in each ${\mathrm{\Omega }}_i$ and nonmatching one across $\partial {\mathrm{\Omega }}_i$. This kind of triangulation and composite discretization are motivated first of all by the regularity of solution of the problem being discussed. The discrete problem is formulated using DG method with interior penalty terms on $\partial {\mathrm{\Omega }}_i$.