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. L (2)-error estimates follow from a discrete Poincar, inequality and an L (aaEuro parts per thousand)-error estimate is given for a P (1)-DDFV solution. Numerical tests and comparison with other schemes (especially those from FVCA5 benchmark) are provided.
discrete duality finite volumes flow problems stability and error estimates numerical tests nonhomogeneous anisotropic media