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arXiv · 2306.05780

A space-time DG method for the Schr\"odinger equation with variable potential

Sergio Gómez·Andrea Moiola
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Abstract

We present a space-time ultra-weak discontinuous Galerkin discretization of the linear Schr\"odinger equation with variable potential. The proposed method is well-posed and quasi-optimal in mesh-dependent norms for very general discrete spaces. Optimal $h$-convergence error estimates are derived for the method when test and trial spaces are chosen either as piecewise polynomials, or as a novel quasi-Trefftz polynomial space. The latter allows for a substantial reduction of the number of degrees of freedom and admits piecewise-smooth potentials. Several numerical experiments validate the accuracy and advantages of the proposed method.

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Sergio Gómez, Andrea Moiola. 2023-06-09. A space-time DG method for the Schr\"odinger equation with variable potential. https://doi.org/10.1007/s10444-024-10108-9

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