Energy conserving Galerkin finite element methods for the Maxwell-Klein-Gordon system

Chupeng Ma, Liqun Cao, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


In this paper, we consider the Galerkin finite element methods for the Maxwell-Klein-Gordon system in the Coulomb gauge. We propose a semidiscrete finite element method for the system with the mixed finite element approximation of the vector potential. Energy conservation and error estimates are established for this scheme. A novel energy conserving time integration scheme is presented for solving the semidiscrete system. The existence and uniqueness of solutions to the fully discrete system are proved under some assumptions. Numerical experiments are carried out to support our theoretical analysis.

Original languageEnglish
Pages (from-to)1339-1366
Number of pages28
JournalSIAM Journal on Numerical Analysis
Issue number2
Publication statusPublished - 29 Apr 2020


  • Energy conservation
  • Error estimates
  • Finite element method
  • Maxwell-Klein-Gordon
  • Time integration scheme

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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