Adv. Appl. Math. Mech., 13 (2021), pp. 791-805.
Published online: 2021-04
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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.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0049}, url = {http://global-sci.org/intro/article_detail/aamm/18751.html} }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.