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Displaying similar documents to “Two-sided a posteriori estimates of global and local errors for linear elliptic type boundary value problems”

On the quality of local flux reconstructions for guaranteed error bounds

Vejchodský, Tomáš

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In this contribution we consider elliptic problems of a reaction-diffusion type discretized by the finite element method and study the quality of guaranteed upper bounds of the error. In particular, we concentrate on complementary error bounds whose values are determined by suitable flux reconstructions. We present numerical experiments comparing the performance of the local flux reconstruction of Ainsworth and Vejchodsky [2] and the reconstruction of Braess and Schöberl [5]. We evaluate...

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...

Two-sided a posteriori error estimates for linear elliptic problems with mixed boundary conditions

Sergey Korotov (2007)

Applications of Mathematics

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The paper is devoted to verification of accuracy of approximate solutions obtained in computer simulations. This problem is strongly related to a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain where such errors are too large and certain mesh refinements should be performed. A mathematical model consisting of a linear elliptic (reaction-diffusion) equation with a mixed Dirichlet/Neumann/Robin boundary condition...

Combined a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces

Sergey I. Repin, Tatiana S. Samrowski, Stéfan A. Sauter (2012)

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

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We consider linear elliptic problems with variable coefficients, which may sharply change values and have a complex behavior in the domain. For these problems, a new combined discretization-modeling strategy is suggested and studied. It uses a sequence of simplified models, approximating the original one with increasing accuracy. Boundary value problems generated by these simplified models are solved numerically, and the approximation and modeling errors are estimated by estimates of...

Combined modeling-discretization error estimate for elliptic problems with complicated interfaces

Sergey I. Repin, Tatiana S. Samrowski, Stéfan A. Sauter (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We consider linear elliptic problems with variable coefficients, which may sharply change values and have a complex behavior in the domain. For these problems, a new combined discretization-modeling strategy is suggested and studied. It uses a sequence of simplified models, approximating the original one with increasing accuracy. Boundary value problems generated by these simplified models are solved numerically, and the approximation and modeling errors are estimated by estimates of...

Combined modeling-discretization error estimate for elliptic problems with complicated interfaces

Sergey I. Repin, Tatiana S. Samrowski, Stéfan A. Sauter (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We consider linear elliptic problems with variable coefficients, which may sharply change values and have a complex behavior in the domain. For these problems, a new combined discretization-modeling strategy is suggested and studied. It uses a sequence of simplified models, approximating the original one with increasing accuracy. Boundary value problems generated by these simplified models are solved numerically, and the approximation and modeling errors are estimated by estimates of...