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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Ivana Šebestová, V. Dolejší (2012)
Acta Universitatis Carolinae. Mathematica et Physica
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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 , 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...
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 , is governed by an elliptic equation and the other, say , by a parabolic-like equation. The underlying application is the poroelasticity system within the quasi-static assumption. Different polynomial orders are used for the - and -components to obtain optimally convergent a priori bounds for all the terms in the error...
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...
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 and magnetization . In [C. Carstensen and A. Prohl, Numer. Math. 90 (2001) 65–99], the conforming -element in spatial dimensions...
Goebbels, St.J. (1999)
Journal of Inequalities and Applications [electronic only]
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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...