A Crank--Nicolson Finite Element Method and the Optimal Error Estimates for the Modified Time-Dependent Maxwell--Schrödinger Equations

DOI10.1137/16M1085231zbMath1382.65322arXiv1703.02281MaRDI QIDQ4603033

Li-qun Cao, Chupeng Ma

Publication date: 14 February 2018

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

Full work available at URL: https://arxiv.org/abs/1703.02281

zbMATH Keywords

algorithmnumerical testoptimal error estimateMaxwell-Schrödinger equationsCrank-Nicolson finite element method

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Maxwell equations (35Q61) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (4)

Chern-Simons-Schrödinger theory on a one-dimensional lattice ⋮ A leap-frog finite element method for wave propagation of Maxwell-Schrödinger equations with nonlocal effect in metamaterials ⋮ Convergence of the Crank-Nicolson extrapolation scheme for the Korteweg-de Vries equation ⋮ The Crank-Nicolson Galerkin method and convergence for the time-dependent Maxwell-Dirac system under the Lorentz gauge

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