论文标题
固定navier-Stokes方程的分布式最佳控制问题的后验错误估计值
A posteriori error estimates for a distributed optimal control problem of the stationary Navier-Stokes equations
论文作者
论文摘要
在两个和三维Lipschitz中，但不一定是凸面，多地域，我们提出和分析了涉及固定的navier的最佳控制问题的后验误差估计器 - stokes方程；还考虑了控制约束。我们制定了两种离散化策略：一个半离散的方案，其中控制变量未被离散化 - 所谓的变异差异方法 - 以及一个完全离散的方案，其中控制控制通过分段二次函数离散。对于每种解决方案技术，我们设计一个A后验误差估计器，可以分解为与状态和伴随方程离散化相关的贡献之和，此外，考虑到完全离散方案时，控制变量的离散化。我们证明了设计的误差估计器是可靠的，并且还探索了局部效率估计。数值实验揭示了基于设计的后验误差估计器的自适应环的竞争性能。
In two and three dimensional Lipschitz, but not necessarily convex, polytopal domains, we propose and analyze a posteriori error estimators for an optimal control problem involving the stationary Navier--Stokes equations; control constraints are also considered. We devise two strategies of discretization: a semi discrete scheme where the control variable is not discretized -- the so-called variational discrezation approach -- and a fully discrete scheme where the control is discretized with piecewise quadratic functions. For each solution solution technique, we design an a posteriori error estimator that can be decomposed as the sum of contributions related to the discretization of the state and adjoint equations and, additionally, the discretization of the control variable for when the fully discrete scheme is considered. We prove that the devised error estimators are reliable and also explore local efficiency estimates. Numerical experiments reveal a competitive performance of adaptive loops based on the devised a posteriori error estimators.
