Volume 13, Issue 4
Error Analysis of Two-Level Finite Element Method for the Nonlinear Conductivity Problem in Maxwell's System

Adv. Appl. Math. Mech., 13 (2021), pp. 791-805.

Published online: 2021-04

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• Abstract

The traditional convergent analysis of two-level method (TLM) will fail when Nedelec 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 Nedelec 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.

• Keywords

Two-level method, nonlinear, conductivity, error estimates, superclose analysis.

65N30, 65N15

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@Article{AAMM-13-791, author = {Peizhen Wang , and Dandan Zhang , and Wei Yang , }, title = {Error Analysis of Two-Level Finite Element Method for the Nonlinear Conductivity Problem in Maxwell's System}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {13}, number = {4}, pages = {791--805}, abstract = {

The traditional convergent analysis of two-level method (TLM) will fail when Nedelec 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 Nedelec 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0049}, url = {http://global-sci.org/intro/article_detail/aamm/18751.html} }
TY - JOUR T1 - Error Analysis of Two-Level Finite Element Method for the Nonlinear Conductivity Problem in Maxwell's System AU - Peizhen Wang , AU - Dandan Zhang , AU - Wei Yang , 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 -

The traditional convergent analysis of two-level method (TLM) will fail when Nedelec 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 Nedelec 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.

Peizhen Wang, Dandan Zhang & Wei Yang. (1970). Error Analysis of Two-Level Finite Element Method for the Nonlinear Conductivity Problem in Maxwell's System. Advances in Applied Mathematics and Mechanics. 13 (4). 791-805. doi:10.4208/aamm.OA-2020-0049
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