A Space-Time Trefftz Discontinuous Galerkin Method for the Linear Schrödinger Equation
نویسندگان
چکیده
A space-time Trefftz discontinuous Galerkin method for the Schr\"odinger equation with piecewise-constant potential is proposed and analyzed. Following spirit of methods, trial test spaces are spanned by non-polynomial complex wave functions that satisfy Schro\"odinger locally on each element mesh. This allows a significant reduction in number degrees freedom comparison full polynomial spaces. We prove well-posedness stability method, and, one- two- dimensional cases, optimal, high-order, h-convergence error estimates skeleton norm. Some numerical experiments validate theoretical results presented.
منابع مشابه
A Trefftz Polynomial Space-Time Discontinuous Galerkin Method for the Second Order Wave Equation
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2022
ISSN: ['0036-1429', '1095-7170']
DOI: https://doi.org/10.1137/21m1426079