In this paper, we investigate the a priori and a posteriori error estimates for the discontinuous Galerkin finite element approximation to a regularization version of the variational inequality of the second kind. We ...In this paper, we investigate the a priori and a posteriori error estimates for the discontinuous Galerkin finite element approximation to a regularization version of the variational inequality of the second kind. We show the optimal error estimates in the DG-norm （stronger than the H1 norm） and the L2 norm, respectively. Furthermore, some residual-based a posteriori error estimators are established which provide global upper bounds and local lower bounds on the discretization error. These a posteriori analysis results can be applied to develop the adaptive DG methods.展开更多
This paper investigated the effects of five kinds of Au surfaces terminated with and without functional groups on the crystallization of ferric oxides/oxyhydroxides in the suspension condition. Self-assembled monolaye...This paper investigated the effects of five kinds of Au surfaces terminated with and without functional groups on the crystallization of ferric oxides/oxyhydroxides in the suspension condition. Self-assembled monolayers （SAMs） were used to create hydroxyl （-OH）, carboxyl （-COOH）, amine （-NH2） and methyl （-CH3） functionalized surfaces, which proved to be of the same surface density. The immersion time of substrates in the Fe（OH）3 suspension was divided into two time portions. During the first period of 2 h, few ferric oxide/oxyhydroxide was deposited except that E-Fe203 was detected on -NH2 surface. Crystallization for 10h evidenced more kinds of iron compounds on the functional surfaces. Goethite and maghemite were noticed on four functional surfaces, and maghemite also grew on Au surface. Deposition of ^-Fe203 was found on -OH surface, while the growth of orthorhombic and hexagon FeOOH were indicated on -NH2 surface. Considering the wide existence of iron compounds in nature, our investigation is a precedent work to the study of iron biomineralization in the suspension area.展开更多
基金Supported by the National Natural Science Foundation of China(No.11071033)
文摘In this paper, we investigate the a priori and a posteriori error estimates for the discontinuous Galerkin finite element approximation to a regularization version of the variational inequality of the second kind. We show the optimal error estimates in the DG-norm （stronger than the H1 norm） and the L2 norm, respectively. Furthermore, some residual-based a posteriori error estimators are established which provide global upper bounds and local lower bounds on the discretization error. These a posteriori analysis results can be applied to develop the adaptive DG methods.
文摘This paper investigated the effects of five kinds of Au surfaces terminated with and without functional groups on the crystallization of ferric oxides/oxyhydroxides in the suspension condition. Self-assembled monolayers （SAMs） were used to create hydroxyl （-OH）, carboxyl （-COOH）, amine （-NH2） and methyl （-CH3） functionalized surfaces, which proved to be of the same surface density. The immersion time of substrates in the Fe（OH）3 suspension was divided into two time portions. During the first period of 2 h, few ferric oxide/oxyhydroxide was deposited except that E-Fe203 was detected on -NH2 surface. Crystallization for 10h evidenced more kinds of iron compounds on the functional surfaces. Goethite and maghemite were noticed on four functional surfaces, and maghemite also grew on Au surface. Deposition of ^-Fe203 was found on -OH surface, while the growth of orthorhombic and hexagon FeOOH were indicated on -NH2 surface. Considering the wide existence of iron compounds in nature, our investigation is a precedent work to the study of iron biomineralization in the suspension area.
