Numerische Mathematik

, Volume 96, Issue 1, pp 17–42

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

Article

DOI: 10.1007/s00211-002-0436-7

Cite this article as:
Achdou, Y., Bernardi, C. & Coquel, F. Numer. Math. (2003) 96: 17. doi:10.1007/s00211-002-0436-7

Summary

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.U.F.R. MathématiquesUniversité Paris VIIParis Cedex 05France
  2. 2.Analyse NumériqueC.N.R.S. & Université Pierre et Marie CurieParis Cedex 05France

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