Mixed Methods for Optimal Control Problems

被引：1
作者：
Hou T. [1 ]
机构：
[1] School of Mathematics and Statistics, Beihua University, Jilin
来源：
Numerical Analysis and Applications | 2018年 / 11卷 / 3期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
a posteriori error estimates; elliptic equations; mixed finite element methods; optimal control problems;
D O I：
10.1134/S1995423918030072
中图分类号：
学科分类号：
摘要：
In this paper, we investigate a posteriori error estimates of amixed finite elementmethod for elliptic optimal control problems with an integral constraint. The gradient for ourmethod belongs to the square integrable space instead of the classical H(div; Ω) space. The state and co-state are approximated by the P0 2-P1 (velocity–pressure) pair and the control variable is approximated by piecewise constant functions. Using duality argument method and energy method, we derive the residual a posteriori error estimates for all variables. © 2018, Pleiades Publishing, Ltd.
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页码：268 / 277
页数：9
相关论文
共 33 条
  • [1] Bonnans J.F., Casas E., An Extension of Pontryagin’s Principle for State-Constrained Optimal Control of Semilinear Elliptic Equations and Variational Inequalities, SIAM J. Contr. Optim., 33, pp. 274-298, (1995)
  • [2] Brunner H., Yan N., Finite Element Methods for Optimal Control Problems Governed by Integral Equations and Integro-Differential Equations, Num. Math., 101, pp. 1-27, (2005)
  • [3] Ciarlet P.G., The Finite Element Method for Elliptic Problems, (1978)
  • [4] Chen Y., Superconvergence of Mixed Finite Element Methods forOptimal Control Problems, Math. Comp., 77, pp. 1269-1291, (2008)
  • [5] Chen Y., Superconvergence of Quadratic Optimal Control Problems by Triangular Mixed Finite Element Methods, Int. J. Num. Meth. Eng., 75, 8, pp. 881-898, (2008)
  • [6] Chen Y., Dai Y., Superconvergence for Optimal Control Problems Governed by Semi-Linear Elliptic Equations, J. Sci. Comput., 39, pp. 206-221, (2009)
  • [7] Chen Y., Huang Y., Liu W.B., Yan N., Error Estimates and Superconvergence ofMixed Finite Element Methods for Convex Optimal Control Problems, J. Sci. Comput., 42, 3, pp. 382-403, (2010)
  • [8] Chen S.C., Chen H.R., New Mixed Element Schemes for a Second-Order Elliptic Problem, Math. Num. Sinica, 32, 2, pp. 213-218, (2010)
  • [9] Gunzburger M.D., Hou L.S., Finite-Dimensional Approximation of a Class of Constrained Nonlinear Optimal Control Problems, SIAM J. Contr. Optim., 34, pp. 1001-1043, (1996)
  • [10] Ge L., Liu W.B., Yang D.P., Adaptive Finite Element Approximation for a ConstrainedOptimal Control Problem via Multi-Meshes, J. Sci. Comput., 41, 2, pp. 238-255, (2009)
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