Convergence of linear finite elements for diffusion equations with measure data

Thierry Gallouët; Raphaèle Herbin

doi:10.1016/j.crma.2003.11.024

Numerical Analysis

Convergence of linear finite elements for diffusion equations with measure data

Presented by: Philippe G. Ciarlet

Thierry Gallouët ¹; Raphaèle Herbin ¹

¹ Université de Provence, 39, rue Joliot-Curie, 13453 Marseille, France

Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 81-84.

Abstract
Résumé

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: 2003-10-23
Accepted: 2003-11-11
Published online: 2003-12-18

DOI: 10.1016/j.crma.2003.11.024

Author's affiliations:

Thierry Gallouët ¹; Raphaèle Herbin ¹

¹ Université de Provence, 39, rue Joliot-Curie, 13453 Marseille, France

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     title = {Convergence of linear finite elements for diffusion equations with measure data},
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     pages = {81--84},
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     language = {en},
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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/

References
Cited by

[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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