TY - JOUR
T1 - Error Analysis of Two-Level Finite Element Method for the Nonlinear Conductivity Problem in Maxwell's System
AU - Wang , Peizhen
AU - Zhang , Dandan
AU - Yang , Wei
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 791
EP - 805
PY - 2021
DA - 2021/04
SN - 13
DO - http://doi.org/10.4208/aamm.OA-2020-0049
UR - https://global-sci.org/intro/article_detail/aamm/18751.html
KW - Two-level method, nonlinear, conductivity, error estimates, superclose analysis.
AB - <p style="text-align: justify;">The traditional convergent analysis of two-level method (TLM) will fail when Nédélec finite element is employed to approximate Maxwell&#39;s system. In this paper, based on the superclose theory, we develop a new analysis framework for the nonlinear conductivity problem in Maxwell&#39;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.</p>