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Richardson extrapolation and defect correction of mixed finite element methods for elliptic optimal control problems

Yanping Chen|Yunqing Huang|Tianliang Hou
대한수학회 (The Korean Mathematical Society)|2012.05|대한수학회지 (Journal of the KMS)|제49권 제3호|pp. 549-569|DOI http://dx.doi.org/

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참고문헌

키워드

asymptotic expansionsoptimal control problemsmixed finite element methodsinterpolation postprocessingdefect correctiona posteriori error estimators
주제분류수학

초록

In this paper asymptotic error expansions for mixed finite element approximations to a class of second order elliptic optimal control problems are derived under rectangular meshes, and the Richardson extrapolation of two different schemes and interpolation defect correction can be applied to increase the accuracy of the approximations. As a by-product, we illustrate that all the approximations of higher accuracy can be used to form a class of a posteriori error estimators of the mixed finite element method for optimal control problems.

Abstract

In this paper asymptotic error expansions for mixed finite element approximations to a class of second order elliptic optimal control problems are derived under rectangular meshes, and the Richardson extrapolation of two different schemes and interpolation defect correction can be applied to increase the accuracy of the approximations. As a by-product, we illustrate that all the approximations of higher accuracy can be used to form a class of a posteriori error estimators of the mixed finite element method for optimal control problems.

참고문헌 (29)

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