AI 中文总结
本文针对 poroelasticity 方程控制的含分布式与 Neumann 边界控制的最优控制问题，采用协调虚拟单元方法，推导适定性与参数一致的误差估计，通过数值实验验证理论结果。
AI 中文摘要
本文研究由线性 poroelasticity 方程控制的最优控制问题的协调虚拟单元方法，考虑分布式控制与 Neumann 边界控制两种情形，采用先优化后离散的方法。通过推导一阶最优性条件，建立三场形式下离散状态与伴随问题的适定性；针对两类控制问题，通过新型 poroelasticity 投影推导最优先验误差估计，该估计对模型问题的相关物理参数一致。此外，采用原始-对偶活动集策略开展数值实验，验证了所得理论结果的正确性。
英文摘要
This paper investigate the conforming virtual element method for the optimal control problem governed by the linear poroelasticity equation. Both distributed control and Neumann boundary controls are considered with the optimize-then-discretize approach. We establish the well-posedness of the discrete state and adjoint problems in three-field formulation by deriving the first-order optimality condition. The optimal a priori error estimates are developed through a novel poroelastic projection for both control problems, and these estimates are uniform with respect to the relevant physical parameters of the model problem. Moreover, the numerical experiments are carried out using the primal dual active set strategy, and demonstrate the support for the derived theoretical results.
