On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation

DOI10.1016/j.aml.2023.108824arXiv2306.09571OpenAlexW4385755608MaRDI QIDQ6052213

Andrea Moiola, Paul Stocker, Sergio Gómez, Ilaria Perugia

Publication date: 21 September 2023

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2306.09571

zbMATH Keywords

discontinuous Galerkin methodSchrödinger equationultra-weak formulationextended Taylor polynomialspolynomial Trefftz space

Mathematics Subject Classification ID

Basic methods for problems in optics and electromagnetic theory (78Mxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Approximations and expansions (41Axx)

Related Items (1)

A space-time DG method for the Schrödinger equation with variable potential

Cites Work

• A space-time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation
• A Space-Time Discontinuous Galerkin Trefftz Method for Time Dependent Maxwell's Equations
• A Trefftz Polynomial Space-Time Discontinuous Galerkin Method for the Second Order Wave Equation
• A Survey of Trefftz Methods for the Helmholtz Equation
• Expansions in Terms of Heat Polynomials and Associated Functions
• Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method
• Introduction to Quantum Mechanics
• Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations
• A Space-Time Trefftz Discontinuous Galerkin Method for the Linear Schrödinger Equation

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