TY - JOUR
T1 - Nonconforming Finite Element Methods for Wave Propagation in Metamaterials
AU - Changhui Yao & Lixiu Wang
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 - <p style="text-align: justify;">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&nbsp;$\mathcal{O}(h^2)$, 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&nbsp;$\mathcal{O}(τ^2 + h^2)$ 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.</p>