Abstract
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 Poincaré inequality and an L ∞ -error estimate is given for a P 1-DDFV solution. Numerical tests and comparison with other schemes (especially those from FVCA5 benchmark) are provided.
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Njifenjou, A., Donfack, H. & Moukouop-Nguena, I. Analysis on general meshes of a discrete duality finite volume method for subsurface flow problems. Comput Geosci 17, 391–415 (2013). https://doi.org/10.1007/s10596-012-9339-6
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DOI: https://doi.org/10.1007/s10596-012-9339-6
Keywords
- Flow problems
- Nonhomogeneous anisotropic media
- Discrete duality finite volumes
- Stability and error estimates
- Numerical tests