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

Chupeng Ma, Liqun Cao, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)2074-2104
Number of pages31
JournalIMA Journal of Numerical Analysis
Volume38
Issue number4
DOIs
Publication statusPublished - 16 Oct 2018

Keywords

  • Crank-Nicolson
  • error estimates
  • Galerkin method
  • Maxwell-Schrödinger

ASJC Scopus subject areas

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

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