Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals

Abstract

Superconvergence of the velocity is established for mimetic finite difference approximations of second-order elliptic problems over $h^2$-uniform quadrilateral meshes. The superconvergence result holds for a full tensor coefficient. The analysis exploits the relation between mimetic finite differences and mixed finite element methods via a special quadrature rule for computing the scalar product in the velocity space. The theoretical results are confirmed by numerical experiments.