Superconvergence of Velocity in Mimetic Finite Difference Methods on Quadrilaterals

Markus Berndt berndt@cut.this.part.lanl.gov

Konstantin Lipnikov lipnikov@cut.this.part.lanl.gov

Mikhail Shashkov shashkov@cut.this.part.lanl.gov

M. F. Wheeler mfw@cut.this.part.ticam.utexas.edu

I. Yotov yotov@cut.this.part.math.pitt.edu

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.