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A priori and a posteriori analysis of finite volume discretizations of Darcy’s equations

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This paper is devoted to the numerical analysis of some finite volume discretizations of Darcy’s equations. We propose two finite volume schemes on unstructured meshes and prove their equivalence with either conforming or nonconforming finite element discrete problems. This leads to optimal a priori error estimates. In view of mesh adaptivity, we exhibit residual type error indicators and prove estimates which allow to compare them with the error in a very accurate way.

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Authors and Affiliations

  1. U.F.R. Mathématiques, Université Paris VII, 2 place Jussieu, 75251, Paris Cedex 05, France

    Y. Achdou

  2. Analyse Numérique, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252, Paris Cedex 05, France

    C. Bernardi & F. Coquel

Authors
  1. Y. Achdou
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  2. C. Bernardi
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  3. F. Coquel
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Corresponding author

Correspondence to C. Bernardi.

Additional information

Mathematics Subject Classification (2000): 65G99, 65M06, 65M15, 65M60, 65P05

This work was partially supported by Contract C03127/AEE2714 with the Laboratoire National d’Hydraulique of the Division Recherche et Développement of Électricité de France. We thank B. Gest and her research group for very interesting discussions on this subject.

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Achdou, Y., Bernardi, C. & Coquel, F. A priori and a posteriori analysis of finite volume discretizations of Darcy’s equations. Numer. Math. 96, 17–42 (2003). https://doi.org/10.1007/s00211-002-0436-7

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  • DOI: https://doi.org/10.1007/s00211-002-0436-7

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