A SPACE-TIME TREFFTZ DISCONTINUOUS GALERKIN METHOD FOR THE LINEAR SCHRODINGER EQUATION

被引：5
|
作者：
GOMEZ, S. E. R. G. I. O. [1 ]
MOIOLA, A. N. D. R. E. A. [1 ]
机构：
[1] Univ Pavia, Dipartimento Matemat, I-27100 Pavia, Italy
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2022年 / 60卷 / 02期
关键词：
linear Schrodinger equation; Trefftz method; discontinuous Galerkin method; a priori error estimate; h-convergence; nonpolynomial basis functions;
D O I：
10.1137/21M1426079
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A space-time Trefftz discontinuous Galerkin method for the Schrodinger equation with piecewise-constant potential is proposed and analyzed. Following the spirit of Trefftz methods, trial and test spaces are spanned by nonpolynomial complex wave functions that satisfy the Schrodinger 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.
引用
收藏
页码：688 / 714
页数：27
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