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Volume 5, Issue 1
A Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control Problems

Yanping Chen & Zhuoqing Lin

East Asian J. Appl. Math., 5 (2015), pp. 85-108.

Published online: 2018-02

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  • Abstract

A posteriori error estimates of semidiscrete mixed finite element methods for quadratic optimal control problems involving linear parabolic equations are developed. The state and co-state are discretised by Raviart-Thomas mixed finite element spaces of order $k$, and the control is approximated by piecewise polynomials of order $k$ ($k≥0$). We derive our a posteriori error estimates for the state and the control approximations via a mixed elliptic reconstruction method. These estimates seem to be unavailable elsewhere in the literature, although they represent an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

  • AMS Subject Headings

49J20, 65N30

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-5-85, author = {Yanping Chen and Zhuoqing Lin}, title = {A Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {5}, number = {1}, pages = {85--108}, abstract = {

A posteriori error estimates of semidiscrete mixed finite element methods for quadratic optimal control problems involving linear parabolic equations are developed. The state and co-state are discretised by Raviart-Thomas mixed finite element spaces of order $k$, and the control is approximated by piecewise polynomials of order $k$ ($k≥0$). We derive our a posteriori error estimates for the state and the control approximations via a mixed elliptic reconstruction method. These estimates seem to be unavailable elsewhere in the literature, although they represent an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.010314.110115a}, url = {http://global-sci.org/intro/article_detail/eajam/10781.html} }
TY - JOUR T1 - A Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control Problems AU - Yanping Chen & Zhuoqing Lin JO - East Asian Journal on Applied Mathematics VL - 1 SP - 85 EP - 108 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.010314.110115a UR - https://global-sci.org/intro/article_detail/eajam/10781.html KW - A posteriori error estimates, optimal control problems, parabolic equations, elliptic reconstruction, semidiscrete mixed finite element methods. AB -

A posteriori error estimates of semidiscrete mixed finite element methods for quadratic optimal control problems involving linear parabolic equations are developed. The state and co-state are discretised by Raviart-Thomas mixed finite element spaces of order $k$, and the control is approximated by piecewise polynomials of order $k$ ($k≥0$). We derive our a posteriori error estimates for the state and the control approximations via a mixed elliptic reconstruction method. These estimates seem to be unavailable elsewhere in the literature, although they represent an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

Yanping Chen and Zhuoqing Lin. (2018). A Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control Problems. East Asian Journal on Applied Mathematics. 5 (1). 85-108. doi:10.4208/eajam.010314.110115a
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