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Mathematics of Computation

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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

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
  • Email: laurent@palamida.math.uch.gr
  • Athanasios E. Tzavaras
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • Email: tzavaras@math.wisc.edu
  • 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: https://doi.org/10.1090/S0025-5718-00-01256-4
  • MathSciNet review: 1813140