The Successive Elimination Technique was first used for a similar discrete system arising from Mixed Hybrid Finite Element (MHFE) analysis of flow problems (see: G. We get then a symmetric positive definite system involving exclusively discrete edge pressures. This difficulty is easily overcome with successive elimination of discrete interface fluxes and discrete cell pressures from the system. So MHFV yields more discrete unknowns than the classical cell-centered Finite Volumes. discretization process leads to a discrete system involving discrete cell presssures, discrete edge pressures and fluxes. These ideas consist to threat the Darcy velocity as an unknown function of the same importance as the fluid pressure. This International Conference on Complex Analysis, Partial Differential Equations and Applications held at Yaounde (Cameroon) from 10th to 15th of December 2001 gave us the opportunity to expose new ideas about the finite volume analysis of flow problems in porous media. Introduction We are interested in solving the following nonhomogeneous diffusion equation with Dirichlet's boundary condition and Cauchy's initial value over a polygonal domain Omega ae R 2 : 8 ? ! ? : d dt W Gamma ` A ' Gamma ` A ' = f (t x y) 2 (0 T ) ThetaOmega, W (t x y) = b(t x y) (x y) 2 (0 T ) Theta Read more In particular, we show that the diffusive flux of the numerical solution is convergent to that of the exact solution when the time step is about the same as the space discretization size.

Furthermore, we provide a complete analysis of. We implemented our method in MATLAB and our numerical experiments show that this method compares favorably against the linear finite element method as implemented by the MATLAB PDE toolbox. We use bivariate C 1 cubic splines (i.e., Fraeijs de Veubeke and Sander's finite elements) to solve nonhomogeneous diffusion equations over polygonal domains.

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