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

doi:10.1007/978-3-319-57397-7_30

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

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

3 Citations (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 language	English
Title of host publication	Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects
Editors	Clément Cancès, Pascal Omnes
Place of Publication	Cham Switzerland
Publisher	Springer
Pages	371-379
Number of pages	9
Volume	199
ISBN (Electronic)	9783319573977
ISBN (Print)	9783319573960
DOIs	https://doi.org/10.1007/978-3-319-57397-7_30
Publication status	Published - 2017
Event	Finite Volumes for Complex Applications 2017 - Université Lille 1, Lille, France Duration: 12 Jun 2017 → 16 Jun 2017 Conference number: 8th https://link.springer.com/book/10.1007/978-3-319-57394-6 (Proceedings)

Publication series

Name	Springer Proceedings in Mathematics & Statistics
Publisher	Springer International Publishing
Volume	199
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	Finite Volumes for Complex Applications 2017
Abbreviated title	FVCA 2017
Country/Territory	France
City	Lille
Period	12/06/17 → 16/06/17
Other	Theme = Hyperbolic, Elliptic and Parabolic Problems
Internet address	https://link.springer.com/book/10.1007/978-3-319-57394-6 (Proceedings)

Keywords

Error estimate
Gradient discretisation method
Heat equation

Access to Document

10.1007/978-3-319-57397-7_30

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). Springer. https://doi.org/10.1007/978-3-319-57397-7_30

Droniou, J ; Eymard, R ; Gallouët, T. et al. / 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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title = "An error estimate for the approximation of linear parabolic equations by the gradient discretization method",

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.",

keywords = "Error estimate, Gradient discretisation method, Heat equation",

author = "J Droniou and R Eymard and T. Gallou{\"e}t and Cindy Guichard and Raphaele Herbin",

year = "2017",

doi = "10.1007/978-3-319-57397-7_30",

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series = "Springer Proceedings in Mathematics & Statistics",

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pages = "371--379",

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booktitle = "Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects",

note = "Finite Volumes for Complex Applications 2017, FVCA 2017 ; Conference date: 12-06-2017 Through 16-06-2017",

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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. et al.
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 proceeding › Conference Paper › Research › peer-review

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AU - Herbin, Raphaele

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AB - 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.

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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). doi: 10.1007/978-3-319-57397-7_30

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

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Discrete functional analysis: bridging pure and numerical mathematics

Cite this

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

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Projects

Discrete functional analysis: bridging pure and numerical mathematics

Cite this