Multiscale mortar mixed domain decomposition approximations of nonlinear parabolic equations
Multiscale mortar mixed domain decomposition approximations of nonlinear parabolic equations
复制标题
非线性抛物方程的多尺度砂浆混合域分解近似
DOI：
10.1016/j.camwa.2021.06.009
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Dong
中科院分区：
文献类型：
--
作者：
M. Arshad;Eun‐Jae Park;Dong
本文考虑用多尺度砂浆混合法近似求解非线性抛物型偏微分方程。多尺度砂浆混合方法的关键思想是用Dirichlet压力边界条件将区域分解成由界面分隔的小区域。在精细尺度上对各个子域进行独立划分，并采用标准混合方法求解各个局部问题。每个界面按粗尺度划分，并定义了一个有限元空间，以加强通量在砂浆界面上的弱连续性。我们同时考虑了连续时间和离散时间的设置，并导出了标量和通量未知量的最优误差估计。给出了迫击炮压力的误差估计。给出了几个数值结果来证明理论收敛估计。
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.