Abstract This paper analyzes an interface-unfitted numerical method for distributed optimal control problems governed by elliptic interface equations. We follow the variational discretization concept to discretize the optimal control problems and apply a Nitsche-eXtended finite element method to discretize the corresponding state and adjoint equations, where piecewise cut basis functions around the interface are enriched into the standard linear element space. Optimal error estimates of the state, co-state and control in a mesh-dependent norm and the L 2 {L^{2}} norm are derived. Numerical results are provided to verify the theoretical results.

中文翻译：

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椭圆界面方程分布式最优控制问题的一种尼切扩展有限元方法

摘要 本文分析了椭圆界面方程控制的分布式最优控制问题的界面未拟合数值方法。我们遵循变分离散化概念对最优控制问题进行离散化，并应用 Nitsche-eXtended 有限元方法对相应的状态和伴随方程进行离散化，其中界面周围的分段切割基函数被丰富到标准线性元空间中。导出了网格相关范数和 L 2 {L^{2}} 范数中状态、共状态和控制的最佳误差估计。提供了数值结果来验证理论结果。