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Title: A third order linearized BDF scheme for Maxwell's equations with nonlinear conductivity using finite element method
Authors: Yao, CH
Lin, YP 
Wang, C
Kou, YL
Keywords: Maxwell's equations with nonlinear conductivity
Convergence analysis and optimal error estimate
Linearized stability analysis
The third order BDF scheme
Issue Date: 2017
Publisher: Institute for Scientific Computing and Information
Source: International journal of numerical analysis and modeling, 2017, v. 14, no. 4-5, p. 511-531 How to cite?
Journal: International journal of numerical analysis and modeling 
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 Nedelec 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 <= C-0*h(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.
ISSN: 1705-5105
EISSN: 1705-5105
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