Error analysis of a class of semi-discrete schemes for solving the Gross-Pitaevskii equation at low regularity

We analyse a class of time discretizations for solving the Gross-Pitaevskii equation at low-regularity on an arbitrary Lipschitz domain $\Omega \subset \mathbb{R}^d$, $d \le 3$, with a non-smooth potential. We show that these schemes, together with their optimal local error structure, allow for convergence under lower regularity assumptions on both the solution and the potential than is required by classical methods, such as splitting or exponential integrator methods. Moreover, we show convergence in the case of periodic boundary conditions, in any fractional positive Sobolev space $H^{r}$, $r \ge 0$ beyond the more typical $L^2$-error analysis.