求解Stokes方程的一种自适应变分多尺度方法

摘要

针对Stokes方程,本文给出一种新的变分多尺度方法.此方法通过构造特殊投影并采用局部化技巧优化了经典变分多尺度方法.同时,本文对此方法进行了后验误差估计,并给出可靠的后验误差估计子及相应的自适应算法.此自适应变分多尺度方法计算简单且易于程序实现.L型区域问题和方腔流问题的数值结果验证了方法的有效性和稳定性.%This paper presents a new variational multiscale method for the Stokes equations.By constructing a special projection and using the localization technique,this method improves the classical variational multiscale method.Meanwhile,this paper proposes a posteriori error estimate,a reliable error estimator and a corresponding adaptive algorithm for this method.The adaptive variational multiscale method is simple and easy to implement.Numerical results for L-shape and cavity problems verify the efficiency and stability of the proposed method.