The Crank-Nicolson Galerkin method and convergence for the time-dependent Maxwell-Dirac system under the Lorentz gauge

DOI10.1016/j.cam.2021.114007zbMath1482.78011OpenAlexW4200473812MaRDI QIDQ2075952

Yaoyao Fu, Li-qun Cao

Publication date: 16 February 2022

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2021.114007

zbMATH Keywords

error estimatesuperconductorgraphenetopological insulatorCrank-Nicolson Galerkin finite element methodtime-dependent Maxwell-Dirac system

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) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Statistical mechanics of superconductors (82D55) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) 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) Statistical mechanics of nanostructures and nanoparticles (82D80)

Related Items

Conservative second-order accurate finite-difference scheme for the coupled Maxwell-Dirac equations, A conservative fourth-order real space method for the (2+1)D Dirac equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On semi-classical limits of ground states of a nonlinear Maxwell-Dirac system
• On spectral stability of the nonlinear Dirac equation
• On global solutions of the Maxwell-Dirac equations
• Stability theory of solitary waves in the presence of symmetry. I
• On the Maxwell-Dirac equations with zero magnetic field and their solution in two space dimensions
• An overview on linear and nonlinear Dirac equations
• An efficient and stable numerical method for the Maxwell--Dirac system
• Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations
• A time-splitting spectral scheme for the Maxwell-Dirac system
• Algebraic solution for the vector potential in the Dirac equation
• General solutions of Maxwell–Dirac equations in 1+1-dimensional space–time and a spatially confined solution
• Significance of Electromagnetic Potentials in the Quantum Theory
• A class of exact plane wave solutions of the Maxwell–Dirac equations
• Finite Element Methods for Navier-Stokes Equations
• A solitary wave solution of the Maxwell-Dirac equations
• Error estimates of Crank–Nicolson Galerkin method for the time-dependent Maxwell–Schrödinger equations under the Lorentz gauge
• A Crank--Nicolson Finite Element Method and the Optimal Error Estimates for the Modified Time-Dependent Maxwell--Schrödinger Equations
• Maxwell–Dirac Equations in Four-Dimensional Minkowski Space
• Semiclassical asymptotics for the Maxwell–Dirac system
• Energy Conserving Galerkin Finite Element Methods for the Maxwell--Klein--Gordon System
• Existence and concentration of semi-classical solutions for a nonlinear Maxwell-Dirac system
• The cauchy problem for the coupled maxwell and dirac equations
• Properties of the Solutions of the Cauchy Problem for the (Classical) Coupled Maxwell-Dirac Equations in One Space Dimension