We present a space–time ultra-weak discontinuous Galerkin discretization of the linear Schrödinger 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.
A space–time DG method for the Schrödinger equation with variable potential
Moiola, Andrea
2024-01-01
Abstract
We present a space–time ultra-weak discontinuous Galerkin discretization of the linear Schrödinger 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.File in questo prodotto:
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