一种解Dirichlet问题的虚拟区域法及其在广义Stokes问题中的应用

摘要

讨论了求解线性Dirichlet问题的虚拟区域法及其在广义Stokes问题中的应用. 这种方法通过Lagrange乘子技术来处理Dirichlet边界条件，因而非常适用于粘性流动问题中的无滑移边界条件。为提高解的精度，我们根据事后误差估算对网格进行自适应加密。Mini-element 离散被应用于广义Stokes问题的求解。最后，我们给出一些数值结果以验证这种针对Dirichlet边界条件的偏微分程解法。%This paper discusses a fictitious domain method for the linear Dirichlet problem and its applications to the generalized Stokes problem. This method treats Dirichlet boundary condition via a Lagrange multiplier technique and is well suited to the no-slip boundary condition in viscous flow problems. In order to improve the accuracy of solutions, meshes are refined according to the a posteriori error estimate. The mini-element discretization is applied to solve the generalized Stokes problem. Finally, some numerical results to validate this method are presented for partial differential equations with Dirichlet boundary condition.