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Nonconforming Finite Element Methods for Wave Propagation in Metamaterials

Part of:Elliptic equations and systemsPartial differential equations, boundary value problems

Published online by Cambridge University Press:  20 February 2017

Changhui Yao and
Lixiu Wang
Changhui Yao*
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, P. R. China
Lixiu Wang*
Affiliation:
Beijing Computational Science Research Center, Beijing, 100193, P. R. China
*
*Corresponding author. Email addresses:chyao@lsec.cc.ac.cn (C.-H. Yao), lxwang@csrc.ac.cn (L.-X. Wang)
*Corresponding author. Email addresses:chyao@lsec.cc.ac.cn (C.-H. Yao), lxwang@csrc.ac.cn (L.-X. Wang)

Abstract

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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 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 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 phenomena are shown to verify our theories.

Keywords

Wave PropagationMetamaterialsNonconforming Mixed Finite ElementError Estimates

MSC classification

Secondary:65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods65N15: Error bounds35J25: Boundary value problems for second-order elliptic equations

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 1 , February 2017, pp. 145 - 166
Copyright
Copyright © Global-Science Press 2017 

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