A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation

Ivana Šebestová

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Displaying similar documents to “A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation”

A posteriori error estimates of the discontinuous Galerkin method for the heat conduction equation

Ivana Šebestová, V. Dolejší (2012)

Acta Universitatis Carolinae. Mathematica et Physica

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A posteriori error estimates for a nonconforming finite element discretization of the heat equation

Serge Nicaise, Nadir Soualem (2005)

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

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The paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the heat equation in $ℝ^{d}$ , $d = 2$ or 3, using backward Euler’s scheme. For this discretization, we derive a residual indicator, which use a spatial residual indicator based on the jumps of normal and tangential derivatives of the nonconforming approximation and a time residual indicator based on the jump of broken gradients at each time step. Lower and upper bounds form the...

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...

Implicit a posteriori error estimation using patch recovery techniques

Tamás Horváth, Ferenc Izsák (2012)

Open Mathematics

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We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient...

Stabilization methods in relaxed micromagnetism

Stefan A. Funken, Andreas Prohl (2005)

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

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The magnetization of a ferromagnetic sample solves a non-convex variational problem, where its relaxation by convexifying the energy density resolves relevant macroscopic information. The numerical analysis of the relaxed model has to deal with a constrained convex but degenerated, nonlocal energy functional in mixed formulation for magnetic potential $u$ and magnetization $𝐦$ . In [C. Carstensen and A. Prohl, Numer. Math. 90 (2001) 65–99], the conforming $P 1 - {(P 0)}^{d}$ -element in $d = 2, 3$ spatial dimensions...

On the sharpness of a superconvergence estimate in connection with one-dimensional Galerkin-methods.

Goebbels, St.J. (1999)

Journal of Inequalities and Applications [electronic only]

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Error estimation and adaptivity for nonlinear FE analysis

Antonio Huerta, Antonio Rodríguez-Ferran, Pedro Díez (2002)

International Journal of Applied Mathematics and Computer Science

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An adaptive strategy for nonlinear finite-element analysis, based on the combination of error estimation and h-remeshing, is presented. Its two main ingredients are a residual-type error estimator and an unstructured quadrilateral mesh generator. The error estimator is based on simple local computations over the elements and the so-called patches. In contrast to other residual estimators, no flux splitting is required. The adaptive strategy is illustrated by means of a complex nonlinear...