论文标题
一种多尺度的方法，用于异质散装耦合
A multiscale method for heterogeneous bulk-surface coupling
论文作者
论文摘要
在本文中，我们构建和分析了一种多尺度（有限元）方法，以解决异质动态边界条件的抛物线问题。作为起源，我们考虑对系统的重新制定，以使散装和表面动态的离散化。这使我们可以将边界上的多尺度方法与内部的标准拉格朗日方案相结合。我们证明并量化低规度解决方案的明确速率，与异质性的振荡行为无关。结果，可以考虑无法解析精细量表的粗糙离散参数。理论发现是通过许多数值实验（包括具有随机扩散系数的动态边界条件）来证明的。
In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformulation of the system in order to decouple the discretization of bulk and surface dynamics. This allows us to combine multiscale methods on the boundary with standard Lagrangian schemes in the interior. We prove convergence and quantify explicit rates for low-regularity solutions, independent of the oscillatory behavior of the heterogeneities. As a result, coarse discretization parameters, which do not resolve the fine scales, can be considered. The theoretical findings are justified by a number of numerical experiments including dynamic boundary conditions with random diffusion coefficients.
