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

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

Peizhen Wang

Dandan Zhang

Wei Yang

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