We study the iterative algorithm proposed by Armstrong et al. (An iterative method for elliptic problems with rapidly oscillating coefficients, 2018. arXiv preprint arXiv:1803.03551) to solve elliptic equations in divergence form with stochastic stationary coefficients. Such equations display rapidly oscillating coefficients and thus usually require very expensive numerical calculations, while this iterative method is comparatively easy to compute. In this article, we strengthen the estimate for the contraction factor achieved by one iteration of the algorithm. We obtain an estimate that holds uniformly over the initial function in the iteration, and which grows only logarithmically with the size of the domain.

我们研究了Armstrong等人提出的迭代算法。（一种用于求解具有快速振荡系数的椭圆问题的迭代方法，2018年。arXiv预印本arXiv：1803.03551）求解具有随机平稳系数的发散形式的椭圆方程。这样的方程式显示快速振荡的系数，因此通常需要非常昂贵的数值计算，而这种迭代方法则比较容易计算。在本文中，我们加强了通过算法的一次迭代获得的收缩因子的估计。我们获得一个估计，该估计在迭代中均匀地保持在初始函数上，并且仅随域的大小对数增长。