Displaying similar documents to “A posteriori error estimates for a nonconforming finite element discretization of the heat equation”

Guaranteed and robust error estimates for singularly perturbed reaction–diffusion problems

Ibrahim Cheddadi, Radek Fučík, Mariana I. Prieto, Martin Vohralík (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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We derive error estimates for singularly perturbed reaction–diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature...

A posteriori error analysis of Euler-Galerkin approximations to coupled elliptic-parabolic problems

Alexandre Ern, Sébastien Meunier (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We analyze Euler-Galerkin approximations (conforming finite elements in space and implicit Euler in time) to coupled PDE systems in which one dependent variable, say u , is governed by an elliptic equation and the other, say p , by a parabolic-like equation. The underlying application is the poroelasticity system within the quasi-static assumption. Different polynomial orders are used for the u - and p -components to obtain optimally convergent a priori bounds for all the terms in the error...

Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients

Stefano Berrone (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this work we derive a posteriori error estimates based on equations residuals for the heat equation with discontinuous diffusivity coefficients. The estimates are based on a fully discrete scheme based on conforming finite elements in each time slab and on the A-stable θ -scheme with 1 / 2 ≤ θ ≤ 1 . Following remarks of [Picasso, Comput. Methods Appl. Mech. Engrg. 167 (1998) 223–237; Verfürth, Calcolo 40 (2003) 195–212] it is easy to identify a time-discretization error-estimator and a space-discretization...

Skipping transition conditions in error estimates for finite element discretizations of parabolic equations

Stefano Berrone (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we derive error estimates for the heat equation. The time discretization strategy is based on a -method and the mesh used for each time-slab is independent of the mesh used for the previous time-slab. The novelty of this paper is an upper bound for the error caused by the coarsening of the mesh used for computing the solution in the previous time-slab. The technique applied for deriving this upper bound is independent of the problem and can be generalized to other time...

A posteriori error control for the Allen–Cahn problem : circumventing Gronwall’s inequality

Daniel Kessler, Ricardo H. Nochetto, Alfred Schmidt (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Phase-field models, the simplest of which is Allen–Cahn’s problem, are characterized by a small parameter ε that dictates the interface thickness. These models naturally call for mesh adaptation techniques, which rely on a posteriori error control. However, their error analysis usually deals with the underlying non-monotone nonlinearity via a Gronwall argument which leads to an exponential dependence on ε - 2 . Using an energy argument combined with a topological continuation argument and...