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Yuri Kuznetsov, Konstantin Lipnikov, and Mikhail Shashkov (2004)

The Mimetic Finite Difference Method On Polygonal Meshes For Diffusion-Type Problems

Computers and Geosciences, Volume 8(4):pp. 301-324.

Mimetic discretizations based on the support-operators method are derived on general polygonal meshes for diffusion-type equations (for instance, equations modeling single phase Darcy flow in porous media). The first order convergence rate for fluid velocity and second-order convergence rate for pressure on general polygonal, locally refined and non-matching meshes are demonstrated with numerical experiments.

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