标题： 对于带有乘性噪声的随机Allen--Cahn方程的全离散SAV格式的强误差估计 显示英文标题

标题： Strong error estimates for a fully discrete SAV scheme for the stochastic Allen--Cahn equation with multiplicative noise

摘要： 我们研究在周期域上具有乘性噪声的随机Allen--Cahn方程的数值逼近。所考虑的方案使用了针对时间离散化的一种最近提出的标量辅助变量方法的增强变体。虽然标量辅助变量方法通常允许构建无条件稳定、高效的线性方案，但所考虑的增强版本（参见[S. Metzger, 2024, IMA J. Numer. Anal.]）还补偿了随机偏微分方程解通常较差的时间正则性，从而扩展了该方案的应用范围。在这项工作中，我们建立了强收敛速率，并表明所提出的线性方案表现出与[A. K. Majee & A. Prohl, 2018, Comput. Methods Appl. Math.]中为非线性结构保持方案建立的相同最优收敛速率。最后，我们提供了验证我们理论结果的数值模拟。 显示英文摘要

摘要： We investigate the numerical approximation of the stochastic Allen--Cahn equation with multiplicative noise on a periodic domain. The considered scheme uses a recently proposed augmented variant of scalar auxiliary variable method for the discretization with respect to time. While scalar auxiliary variable methods in general allow for the construction of unconditionally stable, efficient linear schemes, the considered augmented version (cf. [S. Metzger, 2024, IMA J. Numer. Anal.]) additionally compensates for the typically poor temporal regularity of solutions to stochastic partial differential equations and hence extends the range of applicability of the scheme. In this work, we establish strong rates of convergence and show that the proposed linear scheme exhibits the same optimal rates of convergence that were established in [A. K. Majee & A. Prohl, 2018, Comput. Methods Appl. Math.] for a nonlinear structure preserving scheme. Finally, we provide numerical simulations verifying our theoretical findings.