论文标题
对固定的Navier-Stokes方程和拓扑优化中的应用进行惩罚
Penalization of stationary Navier-Stokes equations and applications in topology optimization
论文作者
论文摘要
我们考虑在Holdall域的子域中，具有混合边界条件的稳定Navier-Stokes系统。我们通过惩罚方法研究其近似特性。还讨论了使用扩展运算符，其他评估和解决方案的唯一性获得的错误估计，当粘度在某些子域中任意较小时。提出了数值测试，包括拓扑优化应用。本文的最后一部分研究了这种类型的几何反向问题和相关最佳控制问题的近似值的一般收敛结果。
We consider the steady Navier-Stokes system with mixed boundary conditions, in subdomains of a holdall domain. We study, via the penalization method, its approximation properties. Error estimates, obtained using the extension operator, other evaluations and the uniqueness of the solution, when the viscosity may be arbitrarily small in certain subdomains, are also discussed. Numerical tests, including topological optimization applications, are presented. A general convergence result for the approximation of this type of geometric inverse problems and of the associated optimal control problems, is investigated in the last part of the paper.
