Convergence Analysis of a DDFD Method for Flow Problems in Homogeneous Porous Media

A new Finite Difference method called Discrete Duality Finite Difference method (DDFD method in short) to solve on quadrilateral meshes 2D-flow problems in homogeneous porous media with full diffusion matrix with constant coefficients is proposed and analyzed in the present work. We start with the derivation of the discrete problem. A result of existence and uniqueness of the solution for that problem is given via the positive definiteness of its associated matrix. Their theoretical p-roperties, namely, stability and error estimates (in discrete energy norm, L²-norm, relative L²-norm, \({{L}^{\infty }}\) -norm), are investigated. Numerical tests are provided.