A Unified Framework for a posteriori Error Estimation in Elliptic and Parabolic Problems with Application to Finite Volumes

Alexandre Ern; Martin Vohralík

doi:10.1007/978-3-642-20671-9_85

A Unified Framework for a posteriori Error Estimation in Elliptic and Parabolic Problems with Application to Finite Volumes

Alexandre Ern
, Martin Vohralík

Sorbonne Université
UPMC Université de Paris VI

Research output: Contribution to journal › Article › peer-review

Abstract

We present a unified framework based on potential and flux reconstruction for guaranteed and efficient a posteriori error estimation. We consider as model problems the Laplace equation, the singularly perturbed convection-diffusion-reaction equation, and the heat equation. The analysis is performed for a wide class of space discretization schemes. Three simple conditions need to be verified, which we do for cell- and vertex-centered finite volumes for all model problems.

Original language	English
Pages (from-to)	821-837
Number of pages	17
Journal	Springer Proceedings in Mathematics
Volume	4
DOIs	https://doi.org/10.1007/978-3-642-20671-9_85
Publication status	Published - 1 Jan 2011

Keywords

a posteriori error estimation
efficiency
elliptic and parabolic problems
guaranteed upper bound
robustness

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10.1007/978-3-642-20671-9_85

Cite this

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AU - Vohralík, Martin

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N2 - We present a unified framework based on potential and flux reconstruction for guaranteed and efficient a posteriori error estimation. We consider as model problems the Laplace equation, the singularly perturbed convection-diffusion-reaction equation, and the heat equation. The analysis is performed for a wide class of space discretization schemes. Three simple conditions need to be verified, which we do for cell- and vertex-centered finite volumes for all model problems.

AB - We present a unified framework based on potential and flux reconstruction for guaranteed and efficient a posteriori error estimation. We consider as model problems the Laplace equation, the singularly perturbed convection-diffusion-reaction equation, and the heat equation. The analysis is performed for a wide class of space discretization schemes. Three simple conditions need to be verified, which we do for cell- and vertex-centered finite volumes for all model problems.

KW - a posteriori error estimation

KW - efficiency

KW - elliptic and parabolic problems

KW - guaranteed upper bound

KW - robustness

UR - https://www.scopus.com/pages/publications/84904132136

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AN - SCOPUS:84904132136

SN - 2190-5614

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JO - Springer Proceedings in Mathematics

JF - Springer Proceedings in Mathematics

ER -

A Unified Framework for a posteriori Error Estimation in Elliptic and Parabolic Problems with Application to Finite Volumes

Abstract

Keywords

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