A Posteriori Error Estimates for Discontinuous Galerkin Time-Stepping Method for Optimal Control Problems Governed by Parabolic Equations

A Posteriori Error Estimates for Discontinuous Galerkin Time-Stepping Method for Optimal Control Problems Governed by Parabolic Equations
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DOI：
10.1137/s0036142902397090
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发表时间：
2004
期刊：
SIAM J. Numer. Anal.
影响因子：
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通讯作者：
Wenbin Liu;He-ping Ma;T. Tang;N. Yan
Wenbin Liu;He-ping Ma;T. Tang;N. Yan
中科院分区：
其他
文献类型：
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作者：
Wenbin Liu;He-ping Ma;T. Tang;N. Yan

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本文研究了线性抛物型方程凸分布最优控制问题的间断Galerkin（DG）有限元逼近，其中间断有限元用于时间离散，协调有限元用于空间离散。我们推导出状态和控制近似的后验误差估计，仅假设空间中的底层网格是非退化的。对于障碍型控制约束的问题，这是最常见的应用中，得到进一步改进的误差估计。
In this paper, we examine the discontinuous Galerkin (DG) finite element approximation to convex distributed optimal control problems governed by linear parabolic equations, where the discontinuous finite element method is used for the time discretization and the conforming finite element method is used for the space discretization. We derive a posteriori error estimates for both the state and the control approximation, assuming only that the underlying mesh in space is nondegenerate. For problems with control constraints of obstacle type, which are the kind most frequently met in applications, further improved error estimates are obtained.