A space-time Trefftz discontinuous Galerkin method for the linear Schr\"odinger equation
Numerical Analysis
2023-10-03 v2 Numerical Analysis
Abstract
A space-time Trefftz discontinuous Galerkin method for the Schr\"odinger equation with piecewise-constant potential is proposed and analyzed. Following the spirit of Trefftz methods, trial and test spaces are spanned by non-polynomial complex wave functions that satisfy the Schro\"odinger equation locally on each element of the space-time mesh. This allows for a significant reduction in the number of degrees of freedom in comparison with full polynomial spaces. We prove well-posedness and stability of the method, and, for the one- and two- dimensional cases, optimal, high-order, h-convergence error estimates in a skeleton norm. Some numerical experiments validate the theoretical results presented.
Keywords
Cite
@article{arxiv.2106.04724,
title = {A space-time Trefftz discontinuous Galerkin method for the linear Schr\"odinger equation},
author = {Sergio Gómez and Andrea Moiola},
journal= {arXiv preprint arXiv:2106.04724},
year = {2023}
}