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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

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Convergence of relaxation schemes to the equations of elastodynamics
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by Laurent Gosse and Athanasios E. Tzavaras PDF
Math. Comp. 70 (2001), 555-577 Request permission


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
  • Email:
  • Athanasios E. Tzavaras
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • Email:
  • 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
  • © Copyright 2000 American Mathematical Society
  • Journal: Math. Comp. 70 (2001), 555-577
  • MSC (2000): Primary 35L65, 65M12
  • DOI:
  • MathSciNet review: 1813140