A second order numerical scheme for nonlinear Maxwell’s equations using conforming finite element

作者：

Highlights：

• Propose a linearized Crank–Nicholson finite element method and derive an optimal L2 error estimate.

• Employ the curl-conforming nature of the Nédelec element makes the numerical solution exactly divergence-free at a discrete level.

• The linearized stability analysis for the numerical error function yields the full order L2 error estimate via an L∞ a-priori assumption at the previous time steps.

• Present some numerical examples to show that the mesh condition is important.

摘要

•Propose a linearized Crank–Nicholson finite element method and derive an optimal L2 error estimate.•Employ the curl-conforming nature of the Nédelec element makes the numerical solution exactly divergence-free at a discrete level.•The linearized stability analysis for the numerical error function yields the full order L2 error estimate via an L∞ a-priori assumption at the previous time steps.•Present some numerical examples to show that the mesh condition is important.

论文关键词：Maxwell’s equations,Nonlinear conductivity,Nédelec finite element method,Error estimate,Linearized stability analysis

论文评审过程：Received 14 August 2018, Revised 27 June 2019, Accepted 24 November 2019, Available online 17 December 2019, Version of Record 17 December 2019.

论文官网地址：https://doi.org/10.1016/j.amc.2019.124940