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Volume 4, Issue 2
Higher Order Triangular Mixed Finite Element Methods for Semilinear Quadratic Optimal Control Problems

Kang Deng, Yanping Chen & Zuliang Lu

DOI: 10.4208/nmtma.2011.42s.4

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 180-196.

Published online: 2011-04

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  • Abstract

In this paper, we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element methods. The state and the co-state are approximated by the order $k$ Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order $k$ ($k\geq 0$). A priori error estimates for the mixed finite element approximation of semilinear control problems are obtained. Finally, we present some numerical examples which confirm our theoretical results.

  • Keywords

A priori error estimates, semilinear optimal control problems, higher order triangular elements, mixed finite element methods.

  • AMS Subject Headings

49J20, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-180, author = {Kang Deng, Yanping Chen and Zuliang Lu}, title = {Higher Order Triangular Mixed Finite Element Methods for Semilinear Quadratic Optimal Control Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {2}, pages = {180--196}, abstract = {

In this paper, we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element methods. The state and the co-state are approximated by the order $k$ Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order $k$ ($k\geq 0$). A priori error estimates for the mixed finite element approximation of semilinear control problems are obtained. Finally, we present some numerical examples which confirm our theoretical results.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.42s.4}, url = {http://global-sci.org/intro/article_detail/nmtma/5964.html} }
TY - JOUR T1 - Higher Order Triangular Mixed Finite Element Methods for Semilinear Quadratic Optimal Control Problems AU - Kang Deng, Yanping Chen & Zuliang Lu JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 180 EP - 196 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.42s.4 UR - https://global-sci.org/intro/article_detail/nmtma/5964.html KW - A priori error estimates, semilinear optimal control problems, higher order triangular elements, mixed finite element methods. AB -

In this paper, we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element methods. The state and the co-state are approximated by the order $k$ Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order $k$ ($k\geq 0$). A priori error estimates for the mixed finite element approximation of semilinear control problems are obtained. Finally, we present some numerical examples which confirm our theoretical results.

Kang Deng, Yanping Chen and Zuliang Lu. (2011). Higher Order Triangular Mixed Finite Element Methods for Semilinear Quadratic Optimal Control Problems. Numerical Mathematics: Theory, Methods and Applications. 4 (2). 180-196. doi:10.4208/nmtma.2011.42s.4
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