Multiscale Modeling &Simulation, Volume 19, Issue 1, Page 374-400, January 2021.
In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As the 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, which are 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.

中文翻译：

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异构体表面耦合的多尺度方法

多尺度建模与仿真，第 19 卷，第 1 期，第 374-400 页，2021 年 1 月。
在本文中，我们构建并分析了具有异构动态边界条件的抛物线问题的多尺度（有限元）方法。作为原点，我们考虑重新制定系统，以解耦体动力学和表面动力学的离散化。这使我们能够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。我们证明了收敛性并量化了低正则性解的显式速率，这与异质性的振荡行为无关。因此，可以考虑不能解决精细尺度的粗离散化参数。大量数值实验证明了理论发现是合理的，包括具有随机扩散系数的动态边界条件。