A third order linearized BDF scheme for Maxwell’s equations with nonlinear conductivity using finite element method

Changhui Yao, Yanping Lin, Cheng Wang, Yanli Kou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)

Abstract

In this paper, we study a third order accurate linearized backward differential formula (BDF) type scheme for the nonlinear Maxwell’s equations, using the Nédelec finite element approximation in space. A purely explicit treatment of the nonlinear term greatly simplifies the computational effort, since we only need to solve a constant-coefficient linear system at each time step. An optimal L2error estimate is presented, via a linearized stability analysis for the numerical error function, under a condition for the time step, τ ≤ C0∗h2for a fixed constant C0∗. Numerical results are provided to confirm our theoretical analysis and demonstrate the high order accuracy and stability (convergence) of the linearized BDF finite element method.
Original languageEnglish
Pages (from-to)511-531
Number of pages21
JournalInternational Journal of Numerical Analysis and Modeling
Volume14
Issue number4-5
Publication statusPublished - 1 Jan 2017

Keywords

  • Convergence analysis and optimal error estimate
  • Linearized stability analysis
  • Maxwell’s equations with nonlinear conductivity
  • The third order BDF scheme

ASJC Scopus subject areas

  • Numerical Analysis

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