Finite element approximation of sparse parabolic control problems
Finite element approximation of sparse parabolic control problems
复制标题
稀疏抛物线控制问题的有限元逼近
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Rösch
中科院分区：
文献类型：
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作者：
E. Casas;M. Mateos;A. Rösch
本文研究了一类半线性偏微分方程最优控制问题的有限元逼近，该问题的目标函数中含有一个促进解的空间稀疏性的项。我们证明了在没有控制界约束的情况下解的存在性，并给出了获得误差估计的充分的二阶条件。对问题进行了完全离散化，得到了离散解的稀疏性和误差估计。
We study the finite element approximation of an optimal control problem governed by a semilinear partial differential equation and whose objective function includes a term promoting space sparsity of the solutions. We prove existence of solution in the absence of control bound constraints and provide the adequate second order sufficient conditions to obtain error estimates. Full discretization of the problem is carried out, and the sparsity properties of the discrete solutions, as well as error estimates, are obtained.