Error estimates of Crank–Nicolson Galerkin method for the time-dependent Maxwell–Schrödinger equations under the Lorentz gauge

DOI10.1093/imanum/drx060zbMath1462.65151arXiv1703.02274OpenAlexW2964350988MaRDI QIDQ4555999

Li-qun Cao, Chupeng Ma, Yan Ping Lin

Publication date: 23 November 2018

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.02274

zbMATH Keywords

Galerkin methoderror estimatesCrank-NicolsonMaxwell-Schrödinger

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Lasers, masers, optical bistability, nonlinear optics (78A60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Electromagnetic theory (general) (78A25)

Related Items (3)

Multiscale Algorithms and Computations for the Time-Dependent Maxwell--Schrödinger System in Heterogeneous Nanostructures ⋮ A leap-frog finite element method for wave propagation of Maxwell-Schrödinger equations with nonlocal effect in metamaterials ⋮ The Crank-Nicolson Galerkin method and convergence for the time-dependent Maxwell-Dirac system under the Lorentz gauge

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