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, convergence analysis and optimal error estimate, linearized stability analysis, the third order BDF scheme.
AB - <p style="text-align: justify;">In this paper, we study a third order accurate linearized backward differential formula
(BDF) type scheme for the nonlinear Maxwell&#39;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 $L^2$ error estimate is presented, via a linearized stability analysis for the numerical
error function, under a condition for the time step, $\tau \leq C^*_0h^2$ 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.</p>