Multiscale asymptotic expansion and a post-processing algorithm for second-order elliptic problems with highly oscillatory coefficients over general convex domains

Authors:
Li-Qun Cao;Jun-Zhi Cui;Jian-Lan Luo
Affiliations:
Institute of Computational Mathematics and Science/Engineering Computing, The Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, P.O. Box 2719, 100080, Beijing, People's ...;Institute of Computational Mathematics and Science/Engineering Computing, The Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, P.O. Box 2719, 100080, Beijing, People's ...;Department of Applied Physics, School of Sciences, Beijing University of Aeronautics and Astronautics, 100083 Beijing, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

Citing 4
Cited 3

Finite element handbook

Finite element handbook
A multiscale finite element method for elliptic problems in composite materials and porous media

Journal of Computational Physics
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients

Mathematics of Computation
Multiscale Asymptotic Analysis and Numerical Simulation for the Second Order Helmholtz Equations with Rapidly Oscillating Coefficients Over General Convex Domains

SIAM Journal on Numerical Analysis

A second-order and two-scale computation method for the quasi-periodic structures of composite materials

Finite Elements in Analysis and Design
A second-order and two-scale computation method for heat conduction equation with rapidly oscillatory coefficients

Finite Elements in Analysis and Design
Multiscale finite element methods for heat equation in three dimension honeycomb structure

AICI'11 Proceedings of the Third international conference on Artificial intelligence and computational intelligence - Volume Part III

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper, we consider the boundary value problem of second-order elliptic type equation with highly oscillatory coefficients over general Lipschitz convex domains, and obtain the multiscale asymptotic expansion of solution for this kind of problem. At the same time, a high accuracy FE computing scheme and a post-processing technique are presented. Finally, numerical results support strongly the theoretical analysis reported in this paper.