A Priori Error Analysis for Finite Element Approximation of Parabolic Optimal Control Problems with Pointwise Control
We consider finite element approximations of parabolic control problems with pointwise control. The state equation exhibits low regularity due to the control imposed pointwisely; this introduces some difficulties for both theoretical and numerical analysis. To discretize the optimal control problem...
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| Veröffentlicht in: | SIAM journal on control and optimization 2014-01, Vol.52 (1), p.97-119 |
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| container_title | SIAM journal on control and optimization |
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| creator | Gong, Wei Hinze, Michael Zhou, Zhaojie |
| description | We consider finite element approximations of parabolic control problems with pointwise control. The state equation exhibits low regularity due to the control imposed pointwisely; this introduces some difficulties for both theoretical and numerical analysis. To discretize the optimal control problem we use variational discretization together with piecewise linear and continuous finite elements for the space discretization of the state, and we use the backward Euler scheme for time discretization. We prove a priori error estimates for the control, state, and adjoint state. Numerical experiments are provided which support the theoretical results. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1137/110840133 |
| format | Article |
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The state equation exhibits low regularity due to the control imposed pointwisely; this introduces some difficulties for both theoretical and numerical analysis. To discretize the optimal control problem we use variational discretization together with piecewise linear and continuous finite elements for the space discretization of the state, and we use the backward Euler scheme for time discretization. We prove a priori error estimates for the control, state, and adjoint state. Numerical experiments are provided which support the theoretical results. 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| ispartof | SIAM journal on control and optimization, 2014-01, Vol.52 (1), p.97-119 |
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| source | SIAM Journals Online |
| subjects | Applied mathematics Approximation Computational mathematics Energy consumption Error analysis Estimates Experiments Mathematical functions |
| title | A Priori Error Analysis for Finite Element Approximation of Parabolic Optimal Control Problems with Pointwise Control |
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