Mixed finite element method for diffusion equations on polygonal meshes with mixed cells

Abstract

In this paper, a new mixed finite element method for the diffusion equation on polygonal meshes is proposed. The method is applied to the diffusion equation on meshes with mixed cells when all the coefficients and the source function may have discontinuities inside polygonal mesh cells. The resulting discrete equations operate only with the degrees of freedom for normal fluxes on the boundaries of cells and one degree of freedom per cell for the solution function.