Asymptotics and an Asymptotic Galerkin Method for Hyperbolic-Parabolic Singular Perturbation Problems

A composite asymptotic expansion including initial layer corrections is developed for treating initial boundary value problems for hyperbolic equations with a small parameter multiplying the second-order time derivative term. Proof of uniform asymptotic validity is given a Hilbert space setting. The...

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Published in:SIAM journal on mathematical analysis Vol. 18; no. 3; pp. 762 - 776
Main Author: Esham, Jr, Benjamin F.
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.05.1987
Subjects:
Approximation
Exact sciences and technology
Hilbert space
Mathematical methods in physics
Numerical approximation and analysis
Physics
Validity
Perturbation theory
Parabolic equation
Boundary value problem
Initial value problem
Hyperbolic equation
Galerkin method
Partial differential equation
ISSN:0036-1410, 1095-7154
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Abstract A composite asymptotic expansion including initial layer corrections is developed for treating initial boundary value problems for hyperbolic equations with a small parameter multiplying the second-order time derivative term. Proof of uniform asymptotic validity is given a Hilbert space setting. The expansion forms the basis of a continuous-time Galerkin procedure for which error analysis based on the finite element method is included. This work extends recent results of Hsiao and Weinacht in two directions, one toward greater abstraction and one toward greater utility.
AbstractList A composite asymptotic expansion including initial layer corrections is developed for treating initial boundary value problems for hyperbolic equations with a small parameter multiplying the second-order time derivative term. Proof of uniform asymptotic validity is given a Hilbert space setting. The expansion forms the basis of a continuous-time Galerkin procedure for which error analysis based on the finite element method is included. This work extends recent results of Hsiao and Weinacht in two directions, one toward greater abstraction and one toward greater utility.
Author Esham, Jr, Benjamin F.
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Cites_doi 10.1080/00036818008839303
10.1016/0022-1236(69)90021-4
10.1016/0022-247X(79)90227-0
10.4064/cm-10-2-331-343
10.1007/BF01236982
10.2140/pjm.1971.36.775
10.1137/0713048
10.2140/pjm.1967.22.213
10.1137/0710062
10.1137/0514091
10.1016/0022-247X(83)90211-1
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Copyright 1987 INIST-CNRS
[Copyright] © 1987 Society for Industrial and Applied Mathematics
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Keywords Perturbation theory
Parabolic equation
Boundary value problem
Initial value problem
Hyperbolic equation
Galerkin method
Partial differential equation
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SubjectTerms Approximation
Exact sciences and technology
Hilbert space
Mathematical methods in physics
Numerical approximation and analysis
Physics
Validity
Title Asymptotics and an Asymptotic Galerkin Method for Hyperbolic-Parabolic Singular Perturbation Problems
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