## 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.## References

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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