Convergence of relaxation schemes to the equations of elastodynamics

Laurent Gosse; Athanasios E. Tzavaras

doi:10.1090/S0025-5718-00-01256-4

Convergence of relaxation schemes to the equations of elastodynamics

Laurent Gosse^*, Athanasios E. Tzavaras

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We study the effect of approximation matrices to semi-discrete relaxation schemes for the equations of one-dimensional elastodynamics. We consider a semi-discrete relaxation scheme and establish convergence using the L^p theory of compensated compactness. Then we study the convergence of an associated relaxation-diffusion system, inspired by the scheme. Numerical comparisons of fully-discrete schemes are carried out.

Original language	English (US)
Pages (from-to)	555-577
Number of pages	23
Journal	MATHEMATICS OF COMPUTATION
Volume	70
Issue number	234
DOIs	https://doi.org/10.1090/S0025-5718-00-01256-4
State	Published - Apr 2001
Externally published	Yes

Keywords

Compensated compactness
Relaxation schemes

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/S0025-5718-00-01256-4

Cite this

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abstract = "We study the effect of approximation matrices to semi-discrete relaxation schemes for the equations of one-dimensional elastodynamics. We consider a semi-discrete relaxation scheme and establish convergence using the Lp theory of compensated compactness. Then we study the convergence of an associated relaxation-diffusion system, inspired by the scheme. Numerical comparisons of fully-discrete schemes are carried out.",

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AU - Tzavaras, Athanasios E.

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AB - We study the effect of approximation matrices to semi-discrete relaxation schemes for the equations of one-dimensional elastodynamics. We consider a semi-discrete relaxation scheme and establish convergence using the Lp theory of compensated compactness. Then we study the convergence of an associated relaxation-diffusion system, inspired by the scheme. Numerical comparisons of fully-discrete schemes are carried out.

KW - Compensated compactness

KW - Relaxation schemes

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JO - MATHEMATICS OF COMPUTATION

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ER -

Convergence of relaxation schemes to the equations of elastodynamics

Abstract

Keywords

ASJC Scopus subject areas

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