A Mortar Mimetic Finite Difference Method on Non-Matching Grids

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

We consider mimetic finite difference approximations to the mixed form of second order elliptic problems on non-matching quadrilateral and triangular multi-block grids. Mortar finite elements are employed on the non-matching interfaces to impose weak continuity of the velocity. Optimal convergence and, for certain cases, superconvergence is established for both the pressure and the velocity.