Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 180-196.
Published online: 2011-04
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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} }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.