标题： Raviart-Thomas空间中的稳定局部正交分解 显示英文标题

标题： Stable localized orthogonal decomposition in Raviart-Thomas spaces

摘要： 本文提出了一种计算多尺度方法，用于求解带齐次Neumann边值条件的二阶线性椭圆型方程的混合形式问题，该方法基于Raviart-Thomas有限元空间中的稳定局部正交分解（LOD）。受数值均匀化思想的启发，构造提供了低维粗近似空间，通过在细网格上求解局部补丁问题，将异质系数的细观信息纳入其中。所得数值格式附有严格的误差分析，并且适用于二维和三维空间中非周期性和非尺度分离的情况。特别是，这种新的实现方式避免了之前混合形式椭圆问题LOD构造中观察到的污染项。最后，提供了多种数值实验以展示该方法的性能。 显示英文摘要

摘要： This work proposes a computational multiscale method for the mixed formulation of a second-order linear elliptic equation subject to a homogeneous Neumann boundary condition, based on a stable localized orthogonal decomposition (LOD) in Raviart-Thomas finite element spaces. In the spirit of numerical homogenization, the construction provides low-dimensional coarse approximation spaces that incorporate fine-scale information from the heterogeneous coefficients by solving local patch problems on a fine mesh. The resulting numerical scheme is accompanied by a rigorous error analysis, and it is applicable beyond periodicity and scale-separation in spatial dimensions two and three. In particular, this novel realization circumvents the presence of pollution terms observed in a previous LOD construction for elliptic problems in mixed formulation. Finally, various numerical experiments are provided that demonstrate the performance of the method.