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Numerical Methods for PDEs: In Occasion of Raytcho Lazarov's 70th Birthday

Yuri Kuznetsov, University of Houston
Discretizations with Piece-Wise Constant Fluxes for Diffusion Equations


In this presentation we discuss a new approach to the discretization of diffusion equations on polygonal/polyhedral meshes. The basic idea is to approximate the solution flux by piece-wise constant vector-functions which are conforming on the interfaces between mesh cells. The error estimate is derived for the solution flux in the case of special types of mesh cells. Numerical results as well as applications in geosciences are given.