A Space-Time Trefftz Discontinuous Galerkin Method for the Linear Schrödinger Equation

DOI10.1137/21M1426079zbMath1491.65093arXiv2106.04724OpenAlexW4220793576WikidataQ114074021 ScholiaQ114074021MaRDI QIDQ5070556

Andrea Moiola, Sergio Gómez

Publication date: 13 April 2022

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.04724

zbMATH Keywords

discontinuous Galerkin methodTrefftz methoda priori error estimatelinear Schrödinger equation\(h\)-convergencenonpolynomial basis functions

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) A priori estimates in context of PDEs (35B45) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation ⋮ Embedded Trefftz discontinuous Galerkin methods ⋮ A space-time DG method for the Schrödinger equation with variable potential

Uses Software

• mctoolbox

Cites Work

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