Efficiency of a posteriori BEM–error estimates for first-kind integral equations on quasi–uniform meshes

Carstensen, Carsten

doi:10.1090/s0025-5718-96-00671-0

Cited by 41 publications

(35 citation statements)

References 30 publications

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“…with smooth Dirichlet data ; see [10] for quasi-uniform meshes and the very recent work [3] for the generalization to locally re ned meshes which are -shape regular (see (3.3b)).…”

Section: Weighted-residual Error Estimatormentioning

confidence: 99%

Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor

Feischl¹,

Führer²,

Mitscha-Eibl

et al. 2014

Computational Methods in Applied Mathematics

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Abstract:We analyze adaptive mesh-re ning algorithms in the frame of boundary element methods (BEM) and the coupling of nite elements and boundary elements (FEM-BEM). Adaptivity is driven by the two-level error estimator proposed by Ernst P. Stephan, Norbert Heuer, and coworkers in the frame of BEM and FEM-BEM or by the residual error estimator introduced by Birgit Faermann for BEM for weakly-singular integral equations. We prove that in either case the usual adaptive algorithm drives the associated error estimator to zero. Emphasis is put on the fact that the error estimators considered are not even globally equivalent to weighted-residual error estimators for which recently convergence with quasi-optimal algebraic rates has been derived.

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“…with smooth Dirichlet data ; see [10] for quasi-uniform meshes and the very recent work [3] for the generalization to locally re ned meshes which are -shape regular (see (3.3b)).…”

Section: Weighted-residual Error Estimatormentioning

confidence: 99%

Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor

Feischl¹,

Führer²,

Mitscha-Eibl

et al. 2014

Computational Methods in Applied Mathematics

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“…We remark that the reverse inequality of (1.3) (with a different constant C) can be proved for uniform grids as in [5].…”

Section: Introductionmentioning

confidence: 98%

An a posteriori error estimate for a first-kind integral equation

Carstensen

1997

Math. Comp.

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Abstract. In this paper we present a new a posteriori error estimate for the boundary element method applied to an integral equation of the first kind. The estimate is local and sharp for quasi-uniform meshes and so improves earlier work of ours. The mesh-dependence of the constants is analyzed and shown to be weaker than expected from our previous work. Besides the Galerkin boundary element method, the collocation method and the qualocation method are considered. A numerical example is given involving an adaptive feedback algorithm.

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“…This issue has been studied by many others [63,64,20,18,19,[29][30][31]. In particular, Faermann [29][30][31] show how to localize fractional Sobolev norms.…”

Section: Introductionmentioning

confidence: 99%

A posteriori error analysis for a class of integral equations and variational inequalities

2010

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We consider elliptic and parabolic variational equations and inequalities governed by integro-differential operators of order 2s ∈ (0, 2]. Our main motivation is the pricing of European or American options under Lévy processes, in particular pure jump processes or jump diffusion processes with tempered stable processes. The problem is discretized using piecewise linear finite elements in space and the implicit Euler method in time. We construct a residual-type a posteriori error estimator which gives a computable upper bound for the actual error in H s -norm. The estimator is localized in the sense that the residuals are restricted to the discrete non-contact region. Numerical experiments illustrate the accuracy of the space and time estimators, and show that they can be used to measure local errors and drive adaptive algorithms.

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Efficiency of a posteriori BEM–error estimates for first-kind integral equations on quasi–uniform meshes

Cited by 41 publications

References 30 publications

Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor

Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor

An a posteriori error estimate for a first-kind integral equation

A posteriori error analysis for a class of integral equations and variational inequalities

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