Analysis on general meshes of a discrete duality finite volume method for subsurface flow problems

This work presents and analyzes, on unstructured grids, a discrete duality finite volume method (DDFV method for short) for 2D-flow problems in nonhomogeneous anisotropic porous media. The derivation of a symmetric discrete problem is established. The existence and uniqueness of a solution to this discrete problem are shown via the positive definiteness of its associated matrix. Properties of this matrix combined with adequate assumptions on data allow to define a discrete energy norm. Stability and error estimate results are proven with respect to this norm. L2-error estimates follow from a discrete Poincaré inequality and an L ∞ -error estimate is given for a P1-DDFV solution. Numerical tests and comparison with other schemes (especially those from FVCA5 benchmark) are provided.