In this paper, nonlinear parabolic partial differential equations are considered to approximate by multiscale mortar mixed method. The key idea of the multiscale mortar mixed approach is to decompose the domain into the smaller subregions separated by the interfaces with the Dirichlet pressure boundary condition. Each subdomain is partitioned independently on the fine scale and the standard mixed methods are used to solve each local problem. Each interface is partitioned on coarse scale and a finite element space is defined to enforce the weak continuity of flux across the mortar interface. We consider both the continuous time and discrete time settings, and derive optimal error estimates for both scalar and flux unknowns. An error estimate for the mortar pressure is also presented. Several numerical results are presented to justify the theoretical convergence estimates.

本文考虑采用多尺度砂浆混合法近似非线性抛物线偏微分方程。多尺度砂浆混合方法的关键思想是将域分解为由具有 Dirichlet 压力边界条件的界面分隔的更小的子区域。每个子域在精细尺度上独立分区，并使用标准混合方法来解决每个局部问题。每个界面都按粗略划分，并定义了一个有限元空间，以加强砂浆界面上通量的弱连续性。我们考虑连续时间和离散时间设置，并为标量和通量未知数得出最佳误差估计。还提供了砂浆压力的误差估计。