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

• Published in: Journal of computational and applied mathematics Vol. 157; no. 1; pp. 1 - 29
• Main Authors: Cao, Li-Qun, Cui, Jun-Zhi, Luo, Jian-Lan
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.08.2003; Elsevier
• Subjects: Exact sciences and technology; Finite element method; Highly oscillatory coefficient; Mathematical analysis; Mathematics; Multiscale asymptotic analysis; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Partial differential equations, boundary value problems; Post-processing technique; Sciences and techniques of general use; Second-order elliptic type equation; Finite element method; 65F10; Second-order elliptic type equation; Post-processing technique; Highly oscillatory coefficient; Multiscale asymptotic analysis; 35B50; Second order equation; Numerical analysis; Elliptic equation; Boundary value problem; Post processing technique; Asymptotic expansion; Multiscale method; Numerical simulation; Partial differential equation
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/S0377-0427(03)00372-8

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.