Error Analysis of Two-Level Finite Element Method for the Nonlinear Conductivity Problem in Maxwell's System
Year: 2021
Author: Peizhen Wang, Dandan Zhang, Wei Yang
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 4 : pp. 791–805
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0049
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 4 : pp. 791–805
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Two-level method nonlinear conductivity error estimates superclose analysis.
Author Details
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