A mortar element method for elliptic problems with discontinuous coefficients

This paper proposes a mortar finite element method for solving the two‐dimensional second‐order elliptic problem with jumps in coefficients across the interface between two subregions. Non‐matching finite element grids are allowed on the interface, so independent triangulations can be used in different subregions. Explicitly realizable mortar conditions are introduced to couple the individual discretizations. The same optimal L
²
‐norm and energy‐norm error estimates as for regular problems are achieved when the interface is of arbitrary shape but smooth, though the regularity of the true solution is low in the whole physical domain.