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

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...

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Published inJournal 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
LanguageEnglish
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
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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.
AbstractList 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.
Author Cao, Li-Qun
Cui, Jun-Zhi
Luo, Jian-Lan
Author_xml – sequence: 1
  givenname: Li-Qun
  surname: Cao
  fullname: Cao, Li-Qun
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  organization: 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 Republic of China
– sequence: 2
  givenname: Jun-Zhi
  surname: Cui
  fullname: Cui, Jun-Zhi
  email: cjz@lsec.cc.ac.cn
  organization: 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 Republic of China
– sequence: 3
  givenname: Jian-Lan
  surname: Luo
  fullname: Luo, Jian-Lan
  organization: Department of Applied Physics, School of Sciences, Beijing University of Aeronautics and Astronautics, 100083 Beijing, People's Republic of China
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Cites_doi 10.1006/jcph.1997.5682
10.1007/BFb0063630
10.1090/S0025-5718-99-01077-7
10.1216/RMJ-1980-10-1-125
10.1137/S0036142900376110
10.1007/978-3-642-61798-0
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Issue 1
Keywords 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
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Snippet In this paper, we consider the boundary value problem of second-order elliptic type equation with highly oscillatory coefficients over general Lipschitz convex...
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SubjectTerms 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
Title Multiscale asymptotic expansion and a post-processing algorithm for second-order elliptic problems with highly oscillatory coefficients over general convex domains
URI https://dx.doi.org/10.1016/S0377-0427(03)00372-8
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