### 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 |
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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 | |

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://indico.math.cnrs.fr/event/1299/overview |

### Publication series

Name | Springer Proceedings in Mathematics & Statistics |
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Publisher | Springer International Publishing |

Volume | 199 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | Finite Volumes for Complex Applications 2017 |
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Abbreviated title | FVCA 8 |

Country | France |

City | Lille |

Period | 12/06/17 → 16/06/17 |

Other | Theme = Hyperbolic, Elliptic and Parabolic Problems |

Internet address |

### Keywords

- Error estimate
- Gradient discretisation method
- Heat equation

### Cite this

*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

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*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.

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

TY - GEN

T1 - An error estimate for the approximation of linear parabolic equations by the gradient discretization method

AU - Droniou, J

AU - Eymard, R

AU - Gallouët, T.

AU - Guichard, Cindy

AU - Herbin, Raphaele

PY - 2017

Y1 - 2017

N2 - 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.

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.

KW - Error estimate

KW - Gradient discretisation method

KW - Heat equation

UR - http://www.scopus.com/inward/record.url?scp=85020485900&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-57397-7_30

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

M3 - Conference Paper

SN - 9783319573960

VL - 199

T3 - Springer Proceedings in Mathematics & Statistics

SP - 371

EP - 379

BT - Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects

A2 - Cancès, Clément

A2 - Omnes, Pascal

PB - Springer

CY - Cham Switzerland

ER -