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The finite volume method for Richards equation

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Abstract

In this paper we prove the convergence of a finite volume scheme for the discretization of an elliptic–parabolic problem, namely Richards equation β(P)t−div(K(β(P))× ∇(P+z))=0, together with Dirichlet boundary conditions and an initial condition. This is done by means of a priori estimates in L2 and the use of Kolmogorov's theorem on relative compactness of subsets of L2.

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Authors and Affiliations

  1. Ecole Nationale des Ponts et Chaussées, 6 et 8 Avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, F-77455, Marne-la-Vallée Cedex 2, France E-mail:

    Robert Eymard

  2. Institut de Recherche Mathématique Avancée, Université Louis Pasteur, 7 rue René Descartes, F-67084, Strasbourg, France E-mail:

    Michaël Gutnic

  3. Laboratoire de Mathématiques, Analyse Numérique et EDP, CNRS et Université de Paris-Sud (bât. 425), F-91405, Orsay Cedex, France E-mail:

    Michaël Gutnic & Danielle Hilhorst

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  1. Robert Eymard
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  2. Michaël Gutnic
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  3. Danielle Hilhorst
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Correspondence to Robert Eymard.

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Eymard, R., Gutnic, M. & Hilhorst, D. The finite volume method for Richards equation. Computational Geosciences 3, 259–294 (1999). https://doi.org/10.1023/A:1011547513583

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