An error estimate for the approximation of linear parabolic equations by the gradient discretization method

J Droniou, R Eymard, T. Gallouët, Cindy Guichard, Raphaele Herbin

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

1 Citation (Scopus)

Abstract

We establish an error estimate for fully discrete time-space gradient schemes on a simple linear parabolic equation. This error estimate holds for all the schemes within the framework of the gradient discretisation method: conforming and non conforming finite element, mixed finite element, hybrid mixed mimetic family, some Multi-Point Flux approximation finite volume scheme and some discontinuous Galerkin schemes.

Original languageEnglish
Title of host publicationFinite Volumes for Complex Applications VIII—Methods and Theoretical Aspects
EditorsClément Cancès, Pascal Omnes
Place of PublicationCham Switzerland
PublisherSpringer
Pages371-379
Number of pages9
Volume199
ISBN (Electronic)9783319573977
ISBN (Print)9783319573960
DOIs
Publication statusPublished - 2017
EventFinite Volumes for Complex Applications 2017 - Université Lille 1, Lille, France
Duration: 12 Jun 201716 Jun 2017
Conference number: 8th
https://indico.math.cnrs.fr/event/1299/overview

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSpringer International Publishing
Volume199
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceFinite Volumes for Complex Applications 2017
Abbreviated titleFVCA 8
CountryFrance
CityLille
Period12/06/1716/06/17
OtherTheme = Hyperbolic, Elliptic and Parabolic Problems
Internet address

Keywords

  • Error estimate
  • Gradient discretisation method
  • Heat equation

Cite this

Droniou, J., Eymard, R., Gallouët, T., Guichard, C., & Herbin, R. (2017). An error estimate for the approximation of linear parabolic equations by the gradient discretization method. In C. Cancès, & P. Omnes (Eds.), Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects (Vol. 199, pp. 371-379). (Springer Proceedings in Mathematics & Statistics; Vol. 199). Cham Switzerland: Springer. https://doi.org/10.1007/978-3-319-57397-7_30
Droniou, J ; Eymard, R ; Gallouët, T. ; Guichard, Cindy ; Herbin, Raphaele. / An error estimate for the approximation of linear parabolic equations by the gradient discretization method. Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects. editor / Clément Cancès ; Pascal Omnes. Vol. 199 Cham Switzerland : Springer, 2017. pp. 371-379 (Springer Proceedings in Mathematics & Statistics).
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Droniou, J, Eymard, R, Gallouët, T, Guichard, C & Herbin, R 2017, An error estimate for the approximation of linear parabolic equations by the gradient discretization method. in C Cancès & P Omnes (eds), Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects. vol. 199, Springer Proceedings in Mathematics & Statistics, vol. 199, Springer, Cham Switzerland, pp. 371-379, Finite Volumes for Complex Applications 2017, Lille, France, 12/06/17. https://doi.org/10.1007/978-3-319-57397-7_30

An error estimate for the approximation of linear parabolic equations by the gradient discretization method. / Droniou, J; Eymard, R; Gallouët, T.; Guichard, Cindy; Herbin, Raphaele.

Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects. ed. / Clément Cancès; Pascal Omnes. Vol. 199 Cham Switzerland : Springer, 2017. p. 371-379 (Springer Proceedings in Mathematics & Statistics; Vol. 199).

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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Droniou J, Eymard R, Gallouët T, Guichard C, Herbin R. An error estimate for the approximation of linear parabolic equations by the gradient discretization method. In Cancès C, Omnes P, editors, Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects. Vol. 199. Cham Switzerland: Springer. 2017. p. 371-379. (Springer Proceedings in Mathematics & Statistics). https://doi.org/10.1007/978-3-319-57397-7_30