RICHARDSON EXTRAPOLATION AND DEFECT CORRECTION OF FINITE ELEMENT METHODS FOR OPTIMAL CONTROL PROBLEMS

被引：5

作者：

Liu, Tang ^{[1
]}

Yan, Ningning ^{[2
]}

Zhang, Shuhua ^{[3
]}

机构：

[1] Tianjin Univ Finance & Econ, Res Ctr Math & Econ, Tianjin 300222, Peoples R China

[2] Chinese Acad Sci, Inst Syst Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[3] Tianjin Univ Finance & Econ, Res Ctr Math & Econ, Tianjin 300222, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2010年 / 28卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Optimal control problem; Finite element methods; Asymptotic error expansions; Defect correction; A posteriori error estimates; BOUNDARY CONTROL-PROBLEMS; VOLTERRA INTEGRODIFFERENTIAL EQUATIONS; PETROV-GALERKIN METHODS; ASYMPTOTIC EXPANSIONS; RECTANGULAR DOMAINS; INTEGRAL-EQUATIONS; ELLIPTIC PROBLEMS; SUPERCONVERGENCE;

D O I：

10.4208/jcm.2009.09-m1001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Asymptotic error expansions in H-1-norm for the bilinear finite element approximation to a class of optimal control problems are derived for rectangular meshes. With the rectangular meshes, the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied. The higher order numerical approximations are used to generate a posteriori error estimators for the finite element approximation.

引用

页码：55 / 71

页数：17

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