Convergence of the mixed finite element method for Maxwell's equations with nonlinear conductivity
Article first published online: 29 JUN 2012
Copyright © 2012 John Wiley & Sons, Ltd.
Mathematical Methods in the Applied Sciences
Volume 35, Issue 13, pages 1489–1504, 15 September 2012
How to Cite
Durand, S. and Slodička, M. (2012), Convergence of the mixed finite element method for Maxwell's equations with nonlinear conductivity. Math. Meth. Appl. Sci., 35: 1489–1504. doi: 10.1002/mma.2513
- Issue published online: 25 JUL 2012
- Article first published online: 29 JUN 2012
- finite elements;
- Maxwell's equations;
- error estimates;
- quasi-static limit
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.