论文标题
具有非标准边界条件的Stokes方程的最小二乘配方 - 一种统一的方法
Least-squares formulations for Stokes equations with non-standard boundary conditions -- A unified approach
论文作者
论文摘要
在本文中，我们提出了一种统一的不合格最小二乘光谱元件方法，用于求解具有各种非标准边界条件的Stokes方程。现有的最小二乘配方主要涉及迪里奇的边界条件，使用基于ADN理论的规律性估计来制定。但是，改变边界条件会导致搜索满足补充和补充条件的参数[4]，这并不容易。在这里，我们避免了基于ADN理论的规律性估计，并提出了一种处理各种边界条件的统一方法。已经讨论了稳定性估计和误差估计。对于具有不同边界条件的两个和三维情况，已经提出了显示指数准确性的数值结果。
In this paper, we propose a unified non-conforming least-squares spectral element approach for solving Stokes equations with various non-standard boundary conditions. Existing least-squares formulations mostly deal with Dirichlet boundary conditions are formulated using ADN theory-based regularity estimates. However, changing boundary conditions lead to a search for parameters satisfying supplementing and complimenting conditions [4] which is not easy always. Here we have avoided ADN theory-based regularity estimates and proposed a unified approach for dealing with various boundary conditions. Stability estimates and error estimates have been discussed. Numerical results displaying exponential accuracy have been presented for both two and three-dimensional cases with various boundary conditions.
