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Volume 1, Issue 2
A Posteriori Error Estimates of Triangular Mixed Finite Element Methods for Semilinear Optimal Control Problems

Zuliang Lu & Yanping Chen

Adv. Appl. Math. Mech., 1 (2009), pp. 242-256.

Published online: 2009-01

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  • Abstract

In this paper, we present an a posteriori error estimates of semilinear quadratic constrained optimal control problems using triangular mixed finite element methods. The state and co-state are approximated by the order $k\leq 1$ Raviart- Thomas mixed finite element spaces and the control is approximated by piecewise constant element. We derive a posteriori error estimates for the coupled state and control approximations. A numerical example is presented in confirmation of the theory.

  • Keywords

Semilinear optimal control problems, mixed finite element methods, a posteriori error estimates.

  • AMS Subject Headings

49J20, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-1-242, author = {Lu , Zuliang and Chen , Yanping}, title = {A Posteriori Error Estimates of Triangular Mixed Finite Element Methods for Semilinear Optimal Control Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {2}, pages = {242--256}, abstract = {

In this paper, we present an a posteriori error estimates of semilinear quadratic constrained optimal control problems using triangular mixed finite element methods. The state and co-state are approximated by the order $k\leq 1$ Raviart- Thomas mixed finite element spaces and the control is approximated by piecewise constant element. We derive a posteriori error estimates for the coupled state and control approximations. A numerical example is presented in confirmation of the theory.

}, issn = {2075-1354}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aamm/8367.html} }
TY - JOUR T1 - A Posteriori Error Estimates of Triangular Mixed Finite Element Methods for Semilinear Optimal Control Problems AU - Lu , Zuliang AU - Chen , Yanping JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 242 EP - 256 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aamm/8367.html KW - Semilinear optimal control problems, mixed finite element methods, a posteriori error estimates. AB -

In this paper, we present an a posteriori error estimates of semilinear quadratic constrained optimal control problems using triangular mixed finite element methods. The state and co-state are approximated by the order $k\leq 1$ Raviart- Thomas mixed finite element spaces and the control is approximated by piecewise constant element. We derive a posteriori error estimates for the coupled state and control approximations. A numerical example is presented in confirmation of the theory.

Zuliang Lu & Yanping Chen. (1970). A Posteriori Error Estimates of Triangular Mixed Finite Element Methods for Semilinear Optimal Control Problems. Advances in Applied Mathematics and Mechanics. 1 (2). 242-256. doi:
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