论文标题
约束能量最小化对流扩散方程的通用多尺度有限元方法
Constraint energy minimizing generalized multiscale finite element method for convection diffusion equation
论文作者
论文摘要
在本文中，我们介绍并分析约束能量最大化对流扩散方程的通用多尺度有限元方法。为了定义多尺度函数，我们首先通过解决以分析促进的本地频谱问题来构建辅助多尺度空间。然后利用在过采样域中执行的约束能量最小化以构建多尺度空间。所得的多尺度函数即使对于高对比度扩散和对流系数也具有良好的衰减特性。此外，如果正确选择了过采样层的数量，我们可以证明收敛速率与粗网格大小成正比。我们的分析还表明，过采样域的大小弱取决于异质系数的对比度。提出了几个数值实验，以说明我们方法的性能。
In this paper we present and analyze a constraint energy minimizing generalized multiscale finite element method for convection diffusion equation. To define the multiscale basis functions, we first build an auxiliary multiscale space by solving local spectral problems motivated by analysis. Then constraint energy minimization performed in oversampling domains is exploited to construct the multiscale space. The resulting multiscale basis functions have a good decay property even for high contrast diffusion and convection coefficients. Furthermore, if the number of oversampling layer is chosen properly, we can prove that the convergence rate is proportional to the coarse mesh size. Our analysis also indicates that the size of the oversampling domain weakly depends on the contrast of the heterogeneous coefficients. Several numerical experiments are presented illustrating the performances of our method.
