Error Analysis of Two-Level Finite Element Method for the Nonlinear Conductivity Problem in Maxwell's System

Abstract

The traditional convergent analysis of two-level method (TLM) will fail when Nédélec finite element is employed to approximate Maxwell's system. In this paper, based on the superclose theory, we develop a new analysis framework for the nonlinear conductivity problem in Maxwell's system, which remedies the weakness of Nédélec finite element for two-level method. This method can save computational cost and improve the efficiency. We obtain the optimal convergent rate $\mathcal{O}(\Delta t+h^2)$ in spatial space. A numerical example verifies our theoretical analysis.