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(τ2+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.
In this paper,Nodal discontinuous Galerkin method is presented to approxi-mate Time-domain Lorentz model equations in meta-materials.The upwind flux is cho-sen in spatial discrete scheme.Low-storage five-stage fourth-order explicit Runge-Kutta method is employed in time discrete scheme.An error estimate of accuracy O(τ^(4)+h^(n))is proved under the L^(2)-norm,specially O(τ^(4)+h^(n+1))can be obtained.Numerical exper-iments for transverse electric(TE)case and transverse magnetic(TM)case are demon-strated to verify the stability and the efficiency of the method in low and higher wave frequency.
In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ｜｜·｜｜div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.
