This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.
This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions.With some criteria,the domain is dynamically decomposed into three parts:kinetic regions where fluids are far from equilibrium,hydrodynamic regions where fluids are near thermodynamical equilibrium and buffer regions which are used as a smooth transition.The Boltzmann-BGK equation is solved in kinetic regions,while Euler equations in hydrodynamic regions and both equations in buffer regions.By a well defined monitor function,our moving mesh method smoothly concentrate the mesh grids to the regions containing rapid variation of the solutions.In each moving mesh step,the solutions are conservatively updated to the new mesh and the cut-off function is rebuilt first to consist with the region decomposition after the mesh motion.In such a framework,the evolution of the hybrid model and the moving mesh procedure can be implemented independently,therefore keep the advantages of both approaches.Numerical examples are presented to demonstrate the efficiency of the method.
In recent years,a nonoverlapping domain decomposition iterative procedure,which is based on using Robin-type boundary conditions as information transmission conditions on the subdomain interfaces,has been developed and analyzed.It is known that the convergence rate of this method is 1-O(h),where h is mesh size.In this paper,the convergence rate is improved to be 1-O(h1/2 H-1/2)sometime by choosing suitable parameter,where H is the subdomain size.Counter examples are constructed to show that our convergence estimates are sharp,which means that the convergence rate cannot be better than 1-O(h1/2H-1/2)in a certain case no matter how parameter is chosen.
