Multiscale asymptotic expansion for second order parabolic equations with rapidly oscillating coefficients

Walter Allegretto; Liqun Cao; Yanping Lin

Multiscale asymptotic expansion for second order parabolic equations with rapidly oscillating coefficients

Walter Allegretto, Liqun Cao, Yanping Lin

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

In this paper we discuss initial-boundary problems for second order parabolic equations with rapidly oscillating coefficients in a bounded convex domain. The asymptotic expansions of the solutions for problems with multiple spatial and temporal scales are presented in four different cases. Higher order corrector methods are constructed and associated explicit convergence rates obtained.

Original language	English
Pages (from-to)	543-576
Number of pages	34
Journal	Discrete and Continuous Dynamical Systems
Volume	20
Issue number	3
Publication status	Published - 1 Mar 2008
Externally published	Yes

Keywords

Asymptotic expansion
Boundary layer
Finite element method
Homogenization
Linear system of differential equation with real periodic coefficients
Parabolic equation with rapidly oscillating coefficients

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

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title = "Multiscale asymptotic expansion for second order parabolic equations with rapidly oscillating coefficients",

abstract = "In this paper we discuss initial-boundary problems for second order parabolic equations with rapidly oscillating coefficients in a bounded convex domain. The asymptotic expansions of the solutions for problems with multiple spatial and temporal scales are presented in four different cases. Higher order corrector methods are constructed and associated explicit convergence rates obtained.",

keywords = "Asymptotic expansion, Boundary layer, Finite element method, Homogenization, Linear system of differential equation with real periodic coefficients, Parabolic equation with rapidly oscillating coefficients",

author = "Walter Allegretto and Liqun Cao and Yanping Lin",

year = "2008",

month = mar,

day = "1",

language = "English",

volume = "20",

pages = "543--576",

journal = "Discrete and Continuous Dynamical Systems",

issn = "1078-0947",

publisher = "American Institute of Mathematical Sciences",

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TY - JOUR

T1 - Multiscale asymptotic expansion for second order parabolic equations with rapidly oscillating coefficients

AU - Allegretto, Walter

AU - Cao, Liqun

AU - Lin, Yanping

PY - 2008/3/1

Y1 - 2008/3/1

N2 - In this paper we discuss initial-boundary problems for second order parabolic equations with rapidly oscillating coefficients in a bounded convex domain. The asymptotic expansions of the solutions for problems with multiple spatial and temporal scales are presented in four different cases. Higher order corrector methods are constructed and associated explicit convergence rates obtained.

AB - In this paper we discuss initial-boundary problems for second order parabolic equations with rapidly oscillating coefficients in a bounded convex domain. The asymptotic expansions of the solutions for problems with multiple spatial and temporal scales are presented in four different cases. Higher order corrector methods are constructed and associated explicit convergence rates obtained.

KW - Asymptotic expansion

KW - Boundary layer

KW - Finite element method

KW - Homogenization

KW - Linear system of differential equation with real periodic coefficients

KW - Parabolic equation with rapidly oscillating coefficients

UR - http://www.scopus.com/inward/record.url?scp=44149107989&partnerID=8YFLogxK

M3 - Journal article

SN - 1078-0947

VL - 20

SP - 543

EP - 576

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 3

ER -

Multiscale asymptotic expansion for second order parabolic equations with rapidly oscillating coefficients

Abstract

Keywords

ASJC Scopus subject areas

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