A New Global Divergence Free and Pressure-Robust HDG Method for Tangential Boundary Control of Stokes Equations
A New Global Divergence Free and Pressure-Robust HDG Method for Tangential Boundary Control of Stokes Equations
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DOI：
10.1016/j.cma.2022.115837
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发表时间：
2022-03
期刊：
影响因子：
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通讯作者：
Gang Chen;W. Gong;M. Mateos;J. Singler;Yangwen Zhang
中科院分区：
文献类型：
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作者：
Gang Chen;W. Gong;M. Mateos;J. Singler;Yangwen Zhang
摘要在Gong et al.（2020），我们提出了一种HDG方法来逼近Stokes方程切向边界控制问题的解，并得到了反映最优控制全局正则性的最优收敛速度.然而，误差估计取决于压力，并且速度不是无发散的。压力鲁棒数值方法对流体的重要性由John等人提出。（2017年）。在这项工作中，我们设计了一个新的HDG方法来近似的解决方案的斯托克斯切向边界控制问题的HDG方法也是独立的利益解决斯托克斯方程。该方案产生了H（div）符合，全球发散自由，和压力鲁棒的解决方案。据我们所知，这是第一次这样的数值方案已获得的最佳边界控制问题的斯托克斯方程。我们也提供了数值实验，以显示新的HDG方法的性能和非压力鲁棒格式的优势。
Abstract In Gong et al.(2020), we proposed an HDG method to approximate the solution of a tangential boundary control problem for the Stokes equations and obtained an optimal convergence rate for the optimal control that reflects its global regularity. However, the error estimates depend on the pressure, and the velocity is not divergence free. The importance of pressure-robust numerical methods for fluids was addressed by John et al.(2017). In this work, we devise a new HDG method to approximate the solution of the Stokes tangential boundary control problem; the HDG method is also of independent interest for solving the Stokes equations. This scheme yields a H (div) conforming, globally divergence free, and pressure-robust solution. To the best of our knowledge, this is the first time such a numerical scheme has been obtained for an optimal boundary control problem for the Stokes equations. We also provide numerical experiments to show the performance of the new HDG method and the advantage over the non pressure-robust scheme.