Finite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state
Finite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state
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DOI：
10.1007/s11081-020-09491-1
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发表时间：
2020-01
影响因子：
2.1
通讯作者：
S. C. Brenner;L. Sung;W. Wollner
中科院分区：
文献类型：
--
作者：
S. C. Brenner;L. Sung;W. Wollner
我们研究一维椭圆分布最优控制问题的有限元方法，对状态导数的点状约束表示为状态变量的四阶变分不等式。对于狄利克雷边界条件问题，我们使用最优状态的现有正则性结果来导出范数中最优状态近似的收敛性。对于具有混合狄利克雷和诺伊曼边界条件的问题，我们证明了最优状态属于对数据的适当假设，并在范数中对最优状态的逼近获得了O(h)收敛性。
We investigatefinite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state formulated as fourth order variational inequalities for the state variable. For the problem with Dirichlet boundary conditions, we use an existingregularity result for the optimal state to deriveconvergence for the approximation of the optimal state in thenorm. For the problem with mixed Dirichlet and Neumann boundary conditions, we show that the optimal state belongs tounder appropriate assumptions on the data and obtainO(h) convergence for the approximation of the optimal state in thenorm.