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Convergence of relaxation schemes to the equations of elastodynamics

Authors: Laurent Gosse and Athanasios E. Tzavaras
Journal: Math. Comp. 70 (2001), 555-577
MSC (2000): Primary 35L65, 65M12
Published electronically: March 24, 2000
MathSciNet review: 1813140
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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 $L^p$ 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.

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Additional Information

Laurent Gosse
Affiliation: Foundation for Research and Technology Hellas / Institute of Applied and Computational Mathematics, P.O. Box 1527, 71110 Heraklion, Crete, Greece
MR Author ID: 611045

Athanasios E. Tzavaras
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

Keywords: Relaxation schemes, compensated compactness
Received by editor(s): March 23, 1999
Published electronically: March 24, 2000
Additional Notes: This joint work was partially supported by TMR project HCL #ERBFMRXCT960033. The second author acknowledges support of the National Science Foundation and the Office for Naval Research
Article copyright: © Copyright 2000 American Mathematical Society