Error estimates of Crank–Nicolson Galerkin method for the time-dependent Maxwell–Schrödinger equations under the Lorentz gauge. (3rd October 2017)

• Record Type: Journal Article
• Authors: Ma, Chupeng; Cao, Liqun; Lin, Yanping
• Is Part Of: IMA journal of numerical analysis. Volume 38:Number 4(2018)
• Page Start: 2074
• Page End: 2104
• Publication Date: 2017-10-03
• Subjects: error estimates -- Crank–Nicolson -- Galerkin method -- Maxwell–Schrödinger; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drx060
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: In this article, we study a numerical method and its convergence for solving the time-dependent Maxwell–Schrödinger equations under the Lorentz gauge. An alternating Crank–Nicolson finite-element method for solving the problem is presented and an optimal error estimate for the numerical algorithm is obtained by a mathematical inductive method. Numerical experiments are then carried out to confirm the theoretical results.