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 L2error estimate is presented, via a linearized stability analysis for the numerical error function, under a condition for the time step, τ ≤ C0∗h2for a fixed constant C0∗. 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.
Original language | English |
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Pages (from-to) | 511-531 |
Number of pages | 21 |
Journal | International Journal of Numerical Analysis and Modeling |
Volume | 14 |
Issue number | 4-5 |
Publication status | Published - 1 Jan 2017 |
Keywords
- Convergence analysis and optimal error estimate
- Linearized stability analysis
- Maxwell’s equations with nonlinear conductivity
- The third order BDF scheme
ASJC Scopus subject areas
- Numerical Analysis