A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension |
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Authors: | Eymard R; Gallouet T; Herbin R |
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Institution: |
1 Université de Marne-la-Vallée, France, 2 Université de Provence, France
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Abstract: | ** Email: eymard{at}math.univ-mlv.fr*** Email: gallouet{at}cmi.univ-mrs.fr**** Corresponding author. Email: herbin{at}cmi.univ-mrs.fr Finite-volume methods for problems involving second-order operatorswith full diffusion matrix can be used thanks to the definitionof a discrete gradient for piecewise constant functions on unstructuredmeshes satisfying an orthogonality condition. This discretegradient is shown to satisfy a strong convergence property forthe interpolation of regular functions, and a weak one for functionsbounded in a discrete H1-norm. To highlight the importance ofboth properties, the convergence of the finite-volume schemefor a homogeneous Dirichlet problem with full diffusion matrixis proven, and an error estimate is provided. Numerical testsshow the actual accuracy of the method. |
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Keywords: | anisotropic diffusion finite-volume methods discrete gradient convergence analysis |
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