Volume 14, Issue 4-5
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

Int. J. Numer. Anal. Mod., 14 (2017), pp. 511-531

Published online: 2017-08

Preview Purchase PDF 4 2569
Export citation
  • 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 L² error estimate is presented, via a linearized stability analysis for the numerical error function, under a condition for the time step, τ ≤ C^*_0h² for a fixed constant C^*_0. 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.

  • Keywords

Maxwell's equations with nonlinear conductivity convergence analysis and optimal error estimate linearized stability analysis the third order BDF scheme

  • AMS Subject Headings

35R35 49J40 60G40

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{IJNAM-14-511, author = {Changhui Yao, Yanping Lin, Cheng Wang and Yanli Kou}, title = {A Third Order Linearized BDF Scheme for Maxwell's Equations with Nonlinear Conductivity Using Finite Element Method.}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {4-5}, pages = {511--531}, 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 L² error estimate is presented, via a linearized stability analysis for the numerical error function, under a condition for the time step, τ ≤ C^*_0h² for a fixed constant C^*_0. 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.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10047.html} }
TY - JOUR T1 - A Third Order Linearized BDF Scheme for Maxwell's Equations with Nonlinear Conductivity Using Finite Element Method. AU - Changhui Yao, Yanping Lin, Cheng Wang & Yanli Kou JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 511 EP - 531 PY - 2017 DA - 2017/08 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10047.html KW - Maxwell's equations with nonlinear conductivity KW - convergence analysis and optimal error estimate KW - linearized stability analysis KW - the third order BDF scheme AB - 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 L² error estimate is presented, via a linearized stability analysis for the numerical error function, under a condition for the time step, τ ≤ C^*_0h² for a fixed constant C^*_0. 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.
Changhui Yao, Yanping Lin, Cheng Wang & Yanli Kou. (1970). A Third Order Linearized BDF Scheme for Maxwell's Equations with Nonlinear Conductivity Using Finite Element Method.. International Journal of Numerical Analysis and Modeling. 14 (4-5). 511-531. doi:
Copy to clipboard
The citation has been copied to your clipboard