Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Superconvergence of the velocity along the Gauss lines in mixed finite element methods
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems
Mathematics of Computation
Quadrilateral H(div) Finite Elements
SIAM Journal on Numerical Analysis
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In this paper we prove some superconvergence of a new family of mixed finite element spaces of higher order which we introduced in [ETNA, Vol. 37, pp. 189-201, 2010]. Among all the mixed finite element spaces having an optimal order of convergence on quadrilateral grids, this space has the smallest unknowns. However, the scalar variable is only suboptimal in general; thus we have employed a post-processing technique for the scalar variable. As a byproduct, we have obtained a superconvergence on a rectangular grid. The superconvergence of a velocity variable naturally holds and can be shown by a minor modification of existing theory, but that of a scalar variable requires a new technique, especially for k=1. Numerical experiments are provided to support the theory.