Comptes Rendus
Numerical Analysis
Convergence of linear finite elements for diffusion equations with measure data
Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 81-84.

We show here the convergence of the linear finite element approximate solutions of a diffusion equation to a weak solution, with weak regularity assumptions on the data.

On prouve la convergence des solutions approchées, par la méthode des éléments finis P1, d'une équation de diffusion avec second membre mesure, vers la solution faible de cette équation.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2003.11.024
Thierry Gallouët 1; Raphaèle Herbin 1

1 Université de Provence, 39, rue Joliot-Curie, 13453 Marseille, France
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Thierry Gallouët; Raphaèle Herbin. Convergence of linear finite elements for diffusion equations with measure data. Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 81-84. doi : 10.1016/j.crma.2003.11.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.11.024/

[1] L. Boccardo; T. Gallouët Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal., Volume 87 (1989), pp. 241-273

[2] P.G. Ciarlet Basic error estimates for elliptic problems, Handbook of Numerical Analysis, vol. II, North-Holland, Amsterdam, 1991, pp. 17-352

[3] J. Droniou, T. Gallouët, R. Herbin, A finite volume scheme for a noncoercive elliptic equation with measure data, SIAM J. Numer. Anal. (2003) in press

[4] R. Eymard, T. Gallouët, R. Herbin, Finite volume methods, in: P.G. Ciarlet, J.-L. Lions (Eds.), Handbook of Numerical Analysis, vol. VII, North-Holland, pp. 713–1020

[5] T. Gallouët; R. Herbin Finite volume methods for diffusion problems and irregular data (F. Benkhaldoun; M. Hänel; R. Vilsmeier, eds.), Finite Volumes for Complex Applications, Problems and Perspectives, II, Hermes, 1999, pp. 155-162

[6] R.A. Nicolaides The covolume approach to computing incompressible flows (M.D. Gunzburger; R.A. Nicolaides, eds.), Incompressible Computational Fluid Dynamics, 1993, pp. 295-333

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