论文标题
抛物线方程中混合配方中的约束能量最小化通用多尺度有限元法
Constraint energy minimization generalized multiscale finite element method in mixed formulation for parabolic equations
论文作者
论文摘要
在本文中，我们在使用异质扩散系数的混合配方中开发了约束能量最小化的通用多尺度有限元法（CEM-GMSFEM）。该方法的构建基于两个多尺度空间：压力多尺度空间和速度多尺度空间。压力空间是通过一组精心设计的局部光谱问题来构建的，可以独立解决。基于计算的压力多尺度空间，我们将通过应用约束能量最小化来构建速度多尺度空间。尤其是，我们证明该方法的收敛性仅取决于粗网格大小，并且与Thediffusion系数的异质性和对比无关。在数值模拟中利用了四种典型类型的渗透率场，结果表明我们所提出的方法效果很好，并提供了有效，准确的数值解。
In this paper, we develop the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) in mixed formulation applied to parabolic equations with heterogeneous diffusion coefficients. The construction of the method is based on two multiscale spaces: pressure multiscale space and velocity multiscale space. The pressure space is constructed via a set of well-designed local spectral problems, which can be solved independently. Based on the computed pressure multiscale space, we will construct the velocity multiscale space by applying constrained energy minimization. The convergence of the proposed method is proved.In particular, we prove that the convergence of the method depends only on the coarse grid size, and is independent of the heterogeneities and contrast of thediffusion coefficient. Four typical types of permeability fields are exploited in the numerical simulations, and the results indicate that our proposed method works well and gives efficient and accurate numerical solutions.
