Volume 10, Issue 1
Nonconforming Finite Element Methods for Wave Propagation in Metamaterials

Changhui Yao & Lixiu Wang

Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 145-166.

Published online: 2017-10

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  • Abstract

In this paper, nonconforming mixed finite element method is proposed to simulate the wave propagation in metamaterials. The error estimate of the semi-discrete scheme is given by convergence order $\mathcal{O}(h^2)$, which is less than 40 percent of the computational costs comparing with the same effect by using Nédélec-Raviart element. A Crank-Nicolson full discrete scheme is also presented with $\mathcal{O}(τ^2 + h^2)$ by traditional discrete formula without using penalty method. Numerical examples of 2D TE, TM cases and a famous re-focusing phenomenon are shown to verify our theories.

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@Article{NMTMA-10-145, author = {}, title = {Nonconforming Finite Element Methods for Wave Propagation in Metamaterials}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2017}, volume = {10}, number = {1}, pages = {145--166}, abstract = {

In this paper, nonconforming mixed finite element method is proposed to simulate the wave propagation in metamaterials. The error estimate of the semi-discrete scheme is given by convergence order $\mathcal{O}(h^2)$, which is less than 40 percent of the computational costs comparing with the same effect by using Nédélec-Raviart element. A Crank-Nicolson full discrete scheme is also presented with $\mathcal{O}(τ^2 + h^2)$ by traditional discrete formula without using penalty method. Numerical examples of 2D TE, TM cases and a famous re-focusing phenomenon are shown to verify our theories.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.m1426}, url = {http://global-sci.org/intro/article_detail/nmtma/12340.html} }
TY - JOUR T1 - Nonconforming Finite Element Methods for Wave Propagation in Metamaterials JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 145 EP - 166 PY - 2017 DA - 2017/10 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.m1426 UR - https://global-sci.org/intro/article_detail/nmtma/12340.html KW - AB -

In this paper, nonconforming mixed finite element method is proposed to simulate the wave propagation in metamaterials. The error estimate of the semi-discrete scheme is given by convergence order $\mathcal{O}(h^2)$, which is less than 40 percent of the computational costs comparing with the same effect by using Nédélec-Raviart element. A Crank-Nicolson full discrete scheme is also presented with $\mathcal{O}(τ^2 + h^2)$ by traditional discrete formula without using penalty method. Numerical examples of 2D TE, TM cases and a famous re-focusing phenomenon are shown to verify our theories.

Changhui Yao & Lixiu Wang. (2020). Nonconforming Finite Element Methods for Wave Propagation in Metamaterials. Numerical Mathematics: Theory, Methods and Applications. 10 (1). 145-166. doi:10.4208/nmtma.2017.m1426
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