Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems. In this study, a rigours convergence analysis is given for such integrators without assuming any restrictive regularity on the solutions or the domains. The analysis is conducted by first deriving a new variational framework for the domain decomposition, which is applicable to the two standard degenerate examples. That is, the p-Laplace and the porous medium type vector fields. Secondly, the decomposed vector fields are restricted to the underlying pivot space and the time integration of the parabolic problem can then be interpreted as an operators splitting applied to a dissipative evolution equation. The convergence results then follow by employing elements of the approximation theory for nonlinear semigroups.

中文翻译：

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退化抛物线方程基于域分解的时间积分器的收敛性分析

基于域分解的时间积分器允许使用并行和分布式硬件，使其非常适合抛物线系统的时间离散化。在本研究中，对此类积分器进行了严格的收敛分析，但不假设解或域有任何限制性规律。该分析首先为域分解推导出一个新的变分框架，该框架适用于两个标准退化示例。即 p-Laplace 和多孔介质类型的矢量场。其次，分解的向量场被限制在潜在的枢轴空间中，抛物线问题的时间积分可以解释为应用于耗散演化方程的算子分裂。