@Article{IJNAM-14-4-5,
author = {},
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 = {<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>},
issn = {2617-8710},
doi = {https://doi.org/2017-IJNAM-10047},
url = {https://global-sci.com/article/83186/a-third-order-linearized-bdf-scheme-for-maxwells-equations-with-nonlinear-conductivity-using-finite-element-method}
}