Superconvergence of mixed finite element approximations to 3-D Maxwell’s equations in metamaterials

Baruch, 2009, Fourth order schemes for time-harmonic wave equations with discontinuous coefficients, Commun. Comput. Phys., 5, 442 Brandts, 1999, Superconvergence of mixed finite element semi-discretization of two time-dependent problems, Appl. Math., 44, 43, 10.1023/A:1022220219953 Chen, 1995 Chen, 2009, Symmetric energy-conserved splitting FDTD scheme for the Maxwell’s equations, Commun. Comput. Phys., 6, 804, 10.4208/cicp.2009.v6.p804 Chen, 2000, Finite element methods with matching and non-matching meshes for Maxwell’s equations with discontinuous coefficients, SIAM J. Numer. Anal., 37, 1542, 10.1137/S0036142998349977 Cockburn, 2004, Locally divergence-free discontinuous Galerkin methods for the Maxwell equations, J. Comput. Phys., 194, 588, 10.1016/j.jcp.2003.09.007 2009 Demkowicz, 2006 Engheta, 2006 Fernandes, 2005, Existence, uniqueness and finite element approximation of the solution of time-harmonic electromagnetic boundary value problems involving metamaterials, COMPEL, 24, 1450, 10.1108/03321640510615724 Fernandes, 2009, Well posedness and finite element approximability of time-harmonic electromagnetic boundary value problems involving bianisotropic materials and metamaterials, Math. Mod. Methods Appl. Sci., 19, 2299, 10.1142/S0218202509004121 Gottlieb, 2001, Strong stability-preserving high-order time discretization methods, SIAM Rev., 43, 89, 10.1137/S003614450036757X Hao, 2008 Hiptmair, 2002, Finite elements in computational electromagnetism, Acta Numer., 11, 237, 10.1017/S0962492902000041 Hesthaven, 2008 Y. Huang, J. Li, Q. Lin, Superconvergence analysis for time-dependent Maxwell’s equations in metamaterials, Numer. Methods Part. Different. Eqs., in press. Li, 2009, Posteriori error estimation for an interiori penalty discontinuous Galerkin method for Maxwell’s equations in cold plasma, Adv. Appl. Math. Mech., 1, 107 Li, 2009, Numerical convergence and physical fidelity analysis for Maxwell’s equations in metamaterials, Comput. Methods Appl. Mech. Engrg., 198, 3161, 10.1016/j.cma.2009.05.018 Li, 2009, Mixed methods using standard conforming finite elements, Comput. Methods Appl. Mech. Engrg., 198, 680, 10.1016/j.cma.2008.10.002 Li, 2007, Finite element analysis for wave propagation in double negative metamaterials, J. Sci. Comput., 32, 263, 10.1007/s10915-007-9131-2 Lin, 2008, Superconvergence analysis for Maxwell’s equations in dispersive media, Math. Comput., 77, 757, 10.1090/S0025-5718-07-02039-X Lin, 1999, Global superconvergence for Maxwell’s equations, Math. Comput., 69, 159, 10.1090/S0025-5718-99-01131-X Lin, 1996 Markos, 2008 Monk, 1994, Superconvergence of finite element approximations to Maxwell’s equations, Numer. Methods Part. Different. Eqs., 10, 793, 10.1002/num.1690100611 Monk, 2003 Nédélec, 1980, Mixed finite elements in R3, Numer. Math., 35, 315, 10.1007/BF01396415 Smith, 2000, Composite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett., 84, 4184, 10.1103/PhysRevLett.84.4184 Veselago, 2006, Negative refractive index materials, J. Comput. Theor. Nanosci., 3, 1, 10.1166/jctn.2006.3000 Wahlbin, 1995 Zhang, 2001, Superconvergent derivative recovery for the intermediate finite element family of the second order, IMA J. Numer. Anal., 21, 643, 10.1093/imanum/21.3.643 Zhong, 2009, Optimal error estimates for Nedelec edge elements for time-harmonic Maxwell’s equations, J. Comput. Math., 27, 563, 10.4208/jcm.2009.27.5.011