Abstract

In this paper, we discuss a priori error estimates and superconvergence of \(P_0^2\)–\(P_1\) mixed finite element methods for elliptic boundary control problems. The state variables and co-state variables are approximated by the\(P_0^2\)–\(P_1\) (velocity-pressure) pair, and the control variable is approximated by piecewise constant functions. First, we derive a priori error estimates for the control variable, the state variables, and the co-state variables. Then we obtain a superconvergence result for the control variable by using a postprocessing projection operator.

中文翻译：

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用于椭圆边界控制问题的 P02-P1 混合有限元方法的先验误差估计和超收敛

摘要

在本文中，我们讨论了\(P_0^2\) - \(P_1\)混合有限元方法对椭圆边界控制问题的先验误差估计和超收敛。状态变量和共态变量由\(P_0^2\) - \(P_1\)（速度-压力）对近似，控制变量由分段常数函数近似。首先，我们推导出控制变量、状态变量和共状态变量的先验误差估计。然后我们通过使用后处理投影算子获得控制变量的超收敛结果。