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Center for Nonlinear Studies |
In this presentation, we discuss a new discretization method for the diffusion equations on general polygonal/polyhedral meshes. The method is based on special approximations of the solution fluxes by piecewise constant finite element vector- functions. The FE vector-functions are conforming on the interfaces between the mesh cells and discontinuous in the interior of the mesh cells. In several important practical cases we derive a simple error estimate for the fluxes. In the final part of the presentation we discuss some application of the method in geosciences and give numerical results for a number of test problems.