Convergence of the mixed finite element method for Maxwell's equations with nonlinear conductivity


S. Durand, Research Group for Numerical Analysis and Mathematical Modelling, Department of Mathematical Analysis, Ghent University, Galglaan 2, Ghent 9000, Belgium.



In this paper, we study a numerical scheme to solve coupled Maxwell's equations with a nonlinear conductivity. This model plays an important role in the study of type-II superconductors. The approximation scheme is based on backward Euler discretization in time and mixed conforming finite elements in space. We will prove convergence of this scheme to the unique weak solution of the problem and develop the corresponding error estimates. As a next step, we study the stability of the scheme in the quasi-static limit ϵ → 0 and present the corresponding convergence rate. Finally, we support the theory by several numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd.