Convergence Analysis on Quadrilateral Grids of a DDFV Method for Subsurface Flow Problems in Anisotropic Heterogeneous Porous Media with Full Neumann Boundary Conditions

Abstract

Our purpose in this paper is to present a theoretical analysis of the Discrete Duality Finite Volume method (DDFV method) for 2D-flow problems in anisotropic heterogeneous porous media with full Neumann boundary conditions. We start with the derivation of the discrete problem, and then we give a result of existence and uniqueness of a solution for that problem. Their theoretical properties, namely stability and error estimates in discrete energy norms and $L^2$-norm are investigated. Numerical tests are provided.