Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an effective scheme for the temporal approximation of such equations, we present a sum splitting scheme that comes with a straightforward parallelization strategy. The convergence analysis is carried out in a variational framework that allows for a general setting and, in particular, nontrivial temporal coefficients. The aim of this work is to illustrate the significant advantages of a variational framework for operator splittings and to use this to extend semigroup-based theory for this type of scheme.

中文翻译：

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和解方案的变分方法

非线性抛物线方程在应用中经常遇到，其求解的有效逼近技术非常重要。为了为此类方程的时间逼近提供有效的方案，我们提出了总和拆分方案，该方案带有直接的并行化策略。收敛分析是在允许总体设置，特别是非平凡的时间系数的变分框架中进行的。这项工作的目的是说明算子拆分的可变框架的显着优势，并使用它来扩展基于半群理论的此类方案。