Title:         Superconvergence of the velocity in mimetic finite difference methods
               on quadrilaterals
Authors:       M. Berndt, K. Lipnikov, M. Shashkov, M. F. Wheeler, and I. Yotov

Source:        SIAM J. Numer. Anal. vol. 43 no. 4 (2005) 1728-1749

Status:        Published

Abstarct: 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.