Zhimin Zhang

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This is the first in a series of papers where a new gradient recovery method is introduced and analyzed. It is proved that the method is superconvergent for translation invariant finite element spaces of any order. The method maintains the simplicity, efficiency, and superconvergence properties of the Zienkiewicz-Zhu patch recovery method. In addition,(More)
The hourly concentrations of BTEX (Benzene, Toluene, Ethylbenzene, m,p-Xylene and o-Xylene) in the urban area of Beijing were measured during July-October 2008, covering the periods of the 2008 Olympic Games and Paralympic Games. The atmospheric BTEX were pre-concentrated on Tenax-TA tubes, and analyzed by GC-PID (Gas Chromatography with Photo Ionization(More)
OBJECTIVES Accumulation of tissue advanced glycation end products (AGEs) is a marker of cumulative glycemic and/or oxidative stress. Cutaneous AGEs levels measured by skin autofluorescence correlate well with cardiovascular outcomes in diabetes and hemodialysis (HD) patients. The present study aimed to compare tissue AGEs levels with peritoneal dialysis(More)
A new, highly sensitive electrochemical immunosensor with a sandwich-type immunoassay format was designed to quantify carcinoembryonic antigen (CEA), as a model tumor marker, using nanogold-enwrapped graphene nanocomposites (NGGNs) as trace labels in clinical immunoassays. The device consisted of a glassy carbon electrode coated with Prussian Blue (PB) on(More)
In this work, the bilinear finite element method on a Shishkin mesh for convection-diffusion problems is analyzed in the two-dimensional setting. A superconvergence rate O(N−2 ln N + N−1.5 lnN) in a discrete -weighted energy norm is established under certain regularity assumptions. This convergence rate is uniformly valid with respect to the singular(More)
Superconvergence phenomenon of the Legendre spectral collocation method and the p-version finite element method is discussed under the one dimensional setting. For a class of functions that satisfy a regularity condition (M): ‖u‖L∞ ≤ cMk on a bounded domain, it is demonstrated, both theoretically and numerically, that the optimal convergent rate is(More)
A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under quadrilateral meshes. It has been proven that the recovered gradient converges at a rate O(h) for ρ = min(α, 1), when the mesh is distorted O(h) (α > 0) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is(More)
Gradient recovery has been widely used for a posteriori error estimates (see Ainsworth & Oden, 2000; Babuška & Strouboulis, 2001; Chen & Xu, 2007; Fierro & Veeser, 2006; Zhang, 2007; Zienkiewicz et al., 2005; Zienkiewicz & Zhu, 1987, 1992a,b). Recently, it has been employed to enhance the eigenvalue approximations by the finite-element method under certain(More)