ABSTRACT

In this paper we discuss a priori error estimates and superconvergence of splitting positive definite mixed finite element methods for optimal control problems governed by pseudo-hyperbolic integro-differential equations. The state variables and co-state variables are approximated by the lowest order Raviart–Thomas mixed finite element functions, and the control variable is approximated by piecewise constant functions. First, we derive a priori error estimates for the control variable, state variables, and co-state variables. Second, we obtain a superconvergence result for the control variable.

中文翻译：

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伪双曲积分微分最优控制问题的分解正定混合有限元方法的先验误差估计和超收敛性

摘要

在本文中，我们讨论了由伪双曲积分微分方程控制的最优控制问题的分解正定混合有限元方法的先验误差估计和超收敛性。状态变量和共状态变量由最低阶Raviart–Thomas混合有限元函数近似，而控制变量由分段常数函数近似。首先，我们导出控制变量，状态变量和共状态变量的先验误差估计。第二，我们获得控制变量的超收敛结果。