Localizations and parallelizations for two-scale finite element discretizations
Fang Liu Aihui Zhou
Some local and parallel algorithms for two-scale finite element discretizations are proposed and analyzed in this paper for elliptic boundary value problems. These algorithms are motivated by the observation that, for a solution to some elliptic boundary value problems, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on partially fine grids by some local procedure. A theoretical tool for analyzing these algorithms is some recent local error estimates for finite element approximations.
keywords: tensor product two-scale discretization. localization parallelization Finite element
Absolutely continuous invariant measures for piecewise $C^2$ and expanding mappings in higher dimensions
Jiu Ding Aihui Zhou
In this paper, by using a trace theorem in the theory of functions of bounded variation, we prove the existence of absolutely continuous invariant measures for a class of piecewise expanding mappings of general bounded domains in any dimension.
keywords: Frobenius-Perron Operators Invariant Measures Variation.

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