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Journal of Scientific Computing

Erschienen in:

01.04.2013

Convergence and Optimality of the Adaptive Nonconforming Linear Element Method for the Stokes Problem

verfasst von: Jun Hu, Jinchao Xu

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2013

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Abstract

In this paper, we analyze the convergence and optimality of a standard adaptive nonconforming linear element method for the Stokes problem. After establishing a special quasi-orthogonality property for both the velocity and the pressure in this saddle point problem, we introduce a new prolongation operator to carry through the discrete reliability analysis for the error estimator. We then use a specially defined interpolation operator to prove that, up to oscillation, the error can be bounded by the approximation error within a properly defined nonlinear approximate class. Finally, by introducing a new parameter-dependent error estimator, we prove the convergence and optimality estimates.

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Titel: Convergence and Optimality of the Adaptive Nonconforming Linear Element Method for the Stokes Problem
verfasst von: Jun Hu
Jinchao Xu
Publikationsdatum: 01.04.2013
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2013
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-012-9625-4

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