A Third Order Linearized BDF Scheme For Maxwell's Equations With Nonlinear Conductivity Using Finite Element Method

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 L² error estimate is presented, via a linearized stability analysis for the numerical error function, under a condition for the time step, ??C₀^*h² for 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.