Superconvergence and Extrapolation Analysis of a Nonconforming Mixed Finite Element Approximation for Time-Harmonic Maxwell’s Equations

Superconvergence Analysis for the Maxwell's Equations in Debye Medium with a Thermal Effect

“…In [31], the authors studied the superconvergence of nonconforming mixed finite element methods for 3-D time-dependent Maxwell's equations in isotropic cold plasma media. In recent years, Maxwell's equations in Debye medium [26][27][28]32] have been studied the convergence and superconvergence properties of the nonconforming finite element. Now stochastic collocation methods for Maxwell's equations with random inputs [10] are becoming another popular issue.…”

Novel methods for the time-dependent Maxwell's equations and their applications

“…As for Maxwell's equations in vacuum, in 1994 Monk carried out the first superconvergence analysis for FEMs in Monk (1994), and for finite difference method together with Süli in Monk and Süli (1994). Later more superconvergence results have been obtained on Cartesian grids solved with edge elements, Lin and Yan (1999); Lin and Li (2008), nonconforming FEMs, Qiao et al (2011); Shi and Pei (2009), discontinuous Galerkin methods, Chung et al (2013), and finite volume methods, Chung et al (2003); Nicolaides and Wang (1998).…”

Nonconforming Mixed Finite Element Method for Time-dependent Maxwell's Equations with ABC

“…In [25], the convergence analysis of Quasi-Wilson nonconforming FE approximation of Maxwell's equations was discussed under arbitrary quasi-uniform quadrilateral meshes. The subsequent work can also be found in [26], where a new mixed nonconforming FE space was constructed and applied to discuss the time-harmonic Maxwell's equations, and the analysis of extrapolation and superconvergence were also studied, respectively. Such these constructions have a same typical advantage, that is, the FEs' consistency errors are one order higher than their interpolation errors.…”