Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 145-166.
Published online: 2017-10
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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} }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.