讲座内容：

In this talk, we present error estimates for a fully discrete filtered Lie splitting scheme applied directly to the Zakharov system, whose solutions may exhibit very low regularity in arbitrary dimensions. Quite remarkably, we observe that the scheme exhibits an \emph{approximately structure-preserving} behavior even in the fully discrete setting. Our analysis relies on multilinear estimates developed within the framework of discrete Bourgain spaces. In particular, we prove that if the exact solution $(E,z,z_t)\in H^{s_c+r+1/2}\times H^{s_c+r}\times H^{s_c+r-1}$, then the numerical error measured in $H^{r+1/2}\times H^{r}\times H^{r-1}$ is of order $\mathcal{O}(\tau^{s_c/2}+N^{-s_c})$ for $s_c\in(0,2]$, where $r=\max(0, d/2-1)$ and $N$ denotes the number of spatial grid points. To the best of our knowledge, this is the first explicit error estimate for a numerical method designed directly for the original Zakharov system, without introducing auxiliary variables or reformulations. Such reformulations typically break the geometric structure of the system, whereas our approach approximately preserves it by working with the system in its original form. Finally, numerical experiments are provided to validate and illustrate our theoretical results.