In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results. 相似文献
The γcmc values of CTAB-SDS decrease from 63.67 mN/m at 10‡C to 36.38 mN/m at 90‡C, slightly lower than those of either CTAB or SDS.
Correspondingly, the CMC of CTAB-SDS decreases almost by half. The increase of surface activity of CTAB-SDS can be attributed
to the relatively weak electrostatic interaction at high temperature, which is supported by the increase of solubility of
CTAB-SDS with rise in temperature. Catalytic effect on oxidation of toluene derivatives with potassium permanganate follows
the order CTAB-SDS > SDS > CTAB. This is not caused by the dissociative effect of CTAB-SDS with low surface activity at low
temperature, as seen from the fact that almost all oxidative products can be retrieved for different toluene derivatives and
surfactants by mimicking the conditions of reaction. In the emulsifications of toluene derivatives at 90‡C, the time that
turbid water layers of surfactant solutions take to become clear is the same as that of the catalytic effect on oxidation
of toluene derivatives. Thus, it can be inferred that surfactants can improve the oxidation yields of toluene derivatives
by increasing the contact between two reacting phases. 相似文献
A simple method is introduced to improve the analysing accuracy of circular groove guide. With this method, the characteristic equation of circular groove guide is derived and its solution is given and discussed.The Project Supported by National Natural Science Foundation of P.R.China 相似文献
We employ a first-principles plane wave method with the
relativistic analytic pseudopotential of Hartwigsen, Goedecker and Hutter
(HGH) scheme in the frame of DFT to calculate
the equilibrium lattice parameters and the thermodynamic properties of
AlB2 compound with hcp structure. The obtained lattice parameters are in
good agreement with the available experimental data and those calculated by
others. Through the quasi-harmonic Debye model, obtained successfully are
the dependences of the
normalized lattice parameters a/a0 and c/c0 on pressure P, the normalized
primitive cell volume V/V0 on pressure P, the variation of the thermal
expansion α with pressure P and temperature T, as well as the Debye
temperature \ThetaD and the heat capacity CV on pressure P and
temperature T. 相似文献
The solar wind almost disappeared on May 11, 1999: the solar wind plasma density and dynamic pressure were less than 1cm−3 and 0.1 nPa respectively, while the interplanetary magnetic field was northward. The polar ionospheric data observed by the multi-instruments at Zhongshan Station in Antarctica on such special event day was compared with those of the control day (May 14). It was shown that geomagnetic activity was very quiet on May 11 at Zhongshan. The magnetic pulsation, which usually occurred at about magnetic noon, did not appear. The ionosphere was steady and stratified, and the F2 layer spread very little. The critical frequency of day-side F2 layer, f0F2, was larger than that of control day, and the peak of f0F2 appeared 2 hours earlier. The ionospheric drift velocity was less than usual. There were intensive auroral Es appearing at magnetic noon. All this indicates that the polar ionosphere was extremely quiet and geomagnetic field was much more dipolar on May 11. There were some signatures of auroral substorm before midnight, such as the negative deviation of the geomagnetic H component, accompanied with auroral Es and weak Pc3 pulsation.
