Finite element approximation for Maxwell’s equations with Debye memory under a nonlinear boundary feedback with delay

Abstract

Numerical analysis is considered for the Maxwell’s equations with Debye memory under a nonlinear boundary feedback with delay. By virtue of finite element method in spatial direction and second-order central difference method in temporal direction, a finite element discrete scheme is established. The stability analysis of the discrete scheme under the assumption τ=λΔt is shown, where λ is a positive integer. Based on the projection operator, the discretization of convolution term and the properties of the nonlinear terms, the error estimate with convergent rate O(Δt2+hs−12) is obtained. Finally, the numerical results are provided to demonstrate the theoretical result.