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An error estimate for the approximation of linear parabolic equations by the Gradient Discretization Method

By Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard and Raphaele Herbin

Abstract

International audienceWe 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 dis-continuous Galerkin schemes

Topics: gradient discretisation method, error estimate, Heat equation, MSC (2010): 65M60, 65M12, [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA]
Publisher: HAL CCSD
Year: 2017
OAI identifier: oai:HAL:hal-01442921v1
Provided by: Hal-Diderot
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