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Displaying similar documents to “An optimal error bound for a finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy”

Complementarity - the way towards guaranteed error estimates

Vejchodský, Tomáš

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This paper presents a review of the complementary technique with the emphasis on computable and guaranteed upper bounds of the approximation error. For simplicity, the approach is described on a numerical solution of the Poisson problem. We derive the complementary error bounds, prove their fundamental properties, present the method of hypercircle, mention possible generalizations and show a couple of numerical examples.

Robust error analysis for the approximation of degree-one Ginzburg-Landau vortices

Sören Bartels (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while...