A finite volume scheme for a noncoercive elliptic equation with measure data

Jérôme Droniou, Thierry Gallouët, Raphaèle Herein

Research output: Contribution to journalArticleResearchpeer-review

21 Citations (Scopus)

Abstract

We show here the convergence of the finite volume approximate solutions of a convection-diffusion equation to a weak solution, without the usual coercitivity assumption on the elliptic operator and with weak regularity assumptions on the data. Numerical experiments are performed to obtain some rates of convergence in two and three space dimensions.

Original languageEnglish
Pages (from-to)1997-2031
Number of pages35
JournalSIAM Journal on Numerical Analysis
Volume41
Issue number6
DOIs
Publication statusPublished - 1 Dec 2003
Externally publishedYes

Keywords

  • Finite volume
  • Measure data
  • Noncoercive elliptic equations

Cite this

Droniou, Jérôme ; Gallouët, Thierry ; Herein, Raphaèle. / A finite volume scheme for a noncoercive elliptic equation with measure data. In: SIAM Journal on Numerical Analysis. 2003 ; Vol. 41, No. 6. pp. 1997-2031.
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A finite volume scheme for a noncoercive elliptic equation with measure data. / Droniou, Jérôme; Gallouët, Thierry; Herein, Raphaèle.

In: SIAM Journal on Numerical Analysis, Vol. 41, No. 6, 01.12.2003, p. 1997-2031.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Droniou, Jérôme

AU - Gallouët, Thierry

AU - Herein, Raphaèle

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N2 - We show here the convergence of the finite volume approximate solutions of a convection-diffusion equation to a weak solution, without the usual coercitivity assumption on the elliptic operator and with weak regularity assumptions on the data. Numerical experiments are performed to obtain some rates of convergence in two and three space dimensions.

AB - We show here the convergence of the finite volume approximate solutions of a convection-diffusion equation to a weak solution, without the usual coercitivity assumption on the elliptic operator and with weak regularity assumptions on the data. Numerical experiments are performed to obtain some rates of convergence in two and three space dimensions.

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KW - Measure data

KW - Noncoercive elliptic equations

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