A Third Order Linearized BDF Scheme for Maxwell's Equations with Nonlinear Conductivity Using Finite Element Method
Year: 2017
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 4-5 : pp. 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 $L^2$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2017-IJNAM-10047
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 4-5 : pp. 511–531
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Maxwell's equations with nonlinear conductivity convergence analysis and optimal error estimate linearized stability analysis the third order BDF scheme.