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In this paper, the Carey nonconforming finite element method (NFEM) for the second order elliptic problem is discussed. By means of the different techniques from the existing literatures, the non-uniform and uniform convergences are obtained only under the lowest regularity assumption on the solution u ∈ H 0 1 Ω. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a new low order least squares nonconforming characteristics mixed finite element method (MFEM) is considered for two-dimensional Burgers’ equation. By use of two typical characters of the elements for approximating the velocity and flux variables: (a) the consistency errors of the elements can be estimated as order with respect to the mesh size h in the broken -norm, one order higher than their interpolation errors; (b) the elements’ interpolation operators satisfy certain orthogonalities, which lead to order error estimates in -norm and some superclose results, the accuracy of corresponding variables in -norm is improved by one order compared with other MFEMs in the existing literature. It seems that the results provided herein have never been derived before. [Copyright &y& Elsevier]

Abstract: In this paper, based on our previous work of asymptotic expansion, an initial effort of global superconvergence analysis of time-domain Maxwell’s equations in isotropic cold plasma media is obtained for semi-discrete mixed finite element scheme. During this procedure, superclose analysis of the interpolation of the smoothing solution and the solution of mixed finite element method is obtained for the first time. By the post-processing operators, superconvergence phenomena can be found. To our best knowledge, this is the first global superconvergence analysis presented by nonconforming mixed finite element methods when isotropic cold plasma media is involved. [Copyright &y& Elsevier]