We study a spatially semidiscrete approximation of nonlinear stochastic partial differential equations (SPDEs) driven by multiplicative noise under weak assumptions on the coefficients avoiding the standard global Lipschitz assumption in the literature. The discretization in space is done by a piecewise linear finite element method. Under some suitable regularity assumption for the exact solution, we present here a rigorous convergence error analysis for the proposed semidiscrete scheme—showing that the numerical scheme admits a convergent rate depending on the regularity of the exact solution.

中文翻译：

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具有非全局Lipschitz连续系数的随机偏微分方程的空间半离散近似的强收敛误差分析

我们研究了在系数较弱的假设下避免了文献中标准的全球Lipschitz假设的情况下，由乘性噪声驱动的非线性随机偏微分方程（SPDE）的空间半离散近似。空间的离散化是通过分段线性有限元方法完成的。在精确解的一些适当正则性假设下，我们在这里对拟议的半离散方案进行严格的收敛误差分析，表明数值方案根据精确解的正则性允许收敛速度。