Goal-oriented <Emphasis Type="Italic">h</Emphasis>-adaptivity for the Helmholtz equation: error estimates,local indicators and refinement strategies |
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Authors: | Lindaura Maria Steffens Núria Parés Pedro Díez |
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Affiliation: | 1.Laboratori de Càlcul Numèric, Departament de Matemàtica Aplicada III,Universitat Politècnica de Catalunya,Barcelona,Spain |
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Abstract: | This paper introduces a new goal-oriented adaptive technique based on a simple and effective post-process of the finite element
approximations. The goal-oriented character of the estimate is achieved by analyzing both the direct problem and an auxiliary
problem, denoted as adjoint or dual problem, which is related to the quantity of interest. Thus, the error estimation technique proposed in this paper would
fall into the category of recovery-type explicit residual a posteriori error estimates. The procedure is valid for general linear quantities of interest and it is also extended to non-linear ones.
The numerical examples demonstrate the efficiency of the proposed approach and discuss: (1) different error representations,
(2) assessment of the dispersion error, and (3) different remeshing criteria. |
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Keywords: | |
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