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 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.