Displaying similar documents to “Estimates of deviations from exact solutions of initial-boundary value problem for the heat equation”

Functional a posteriori error estimates for incremental models in elasto-plasticity

Sergey Repin, Jan Valdman (2009)

Open Mathematics

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We consider incremental problem arising in elasto-plastic models with isotropic hardening. Our goal is to derive computable and guaranteed bounds of the difference between the exact solution and any function in the admissible (energy) class of the problem considered. Such estimates are obtained by an advanced version of the variational approach earlier used for linear boundary-value problems and nonlinear variational problems with convex functionals [24, 30]. They do no contain mesh-dependent...

Estimates of weighted Hölder norms of the solutions to a parabolic boundary value problem in an initially degenerate domain

Antonio Fasano, Vsevolod Solonnikov (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A-priori estimates in weighted Hölder norms are obtained for the solutions of a one- dimensional boundary value problem for the heat equation in a domain degenerating at time t = 0 and with boundary data involving simultaneously the first order time derivative and the spatial gradient.

A finite element discretization of the contact between two membranes

Faker Ben Belgacem, Christine Bernardi, Adel Blouza, Martin Vohralík (2009)

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

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From the fundamental laws of elasticity, we write a model for the contact between two membranes and we perform the analysis of the corresponding system of variational inequalities. We propose a finite element discretization of this problem and prove its well-posedness. We also establish a priori and a posteriori error estimates.

Verification of functional a posteriori error estimates for obstacle problem in 2D

Petr Harasim, Jan Valdman (2014)

Kybernetika

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We verify functional a posteriori error estimates proposed by S. Repin for a class of obstacle problems in two space dimensions. New benchmarks with known analytical solution are constructed based on one dimensional benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the solution of the obstacle problem is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is measured by a functional majorant. The...