Explicit stabilized integrators are an efficient alternative to implicit or semiimplicit methods to avoid the severe time-step restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper we provide a fully discrete strong convergence analysis of a family of explicit stabilized methods coupled with finite element methods for a class of parabolic semilinear deterministic and stochastic partial differential equations. Numerical experiments including the semilinear stochastic heat equation with space-time white noise confirm the theoretical findings.

中文翻译：

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抛物线半线性随机偏微分方程显式稳定积分器的收敛性分析

显式稳定积分器是隐式或半隐式方法的有效替代方法，可避免应用于刚性扩散问题的标准显式积分器面临的严重时间步长限制。在本文中，我们为一类抛物线半线性确定性和随机偏微分方程提供了一系列显式稳定方法与有限元方法的完全离散强收敛性分析。包括时空白噪声的半线性随机热方程在内的数值实验证实了理论发现。