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Convergence of relaxation schemes to the equations of elastodynamics
Author(s):
Laurent
Gosse;
Athanasios
E.
Tzavaras.
Journal:
Math. Comp.
70
(2001),
555-577.
MSC (2000):
Primary 35L65, 65M12
Posted:
March 24, 2000
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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  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
Email:
laurent@palamida.math.uch.gr
Athanasios
E.
Tzavaras
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email:
tzavaras@math.wisc.edu
DOI:
10.1090/S0025-5718-00-01256-4
PII:
S 0025-5718(00)01256-4
Keywords:
Relaxation schemes,
compensated compactness
Received by editor(s):
March 23, 1999
Posted:
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 of article:
Copyright
2000,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Tzavaras, Athanasios E., On the mathematical theory of fluid dynamic limits to conservation laws, Advances in mathematical fluid mechanics (Paseky, 1999), Springer, Berlin, 2000, pp. 192--222.
Chen, Gui-Qiang; Wang, Dehua, The Cauchy problem for the Euler equations for compressible fluids , Handbook of Mathematical Fluid Dynamics, vol. 1, Elsevier, 2002, pp. 421-543.
C. Arvanitis, T. Katsaounis, Ch. Makridakis, Adaptive finite element relaxation schemes for hyperbolic conservation laws, M2AN Math. Model. Numer. Anal. 35 (2001), 17-33. (English)
LeVeque, Randall J.; Pelanti, Marica, A class of approximate Riemann solvers and their relation to relaxation schemes, J. Comput. Phys. 172 (2001), 572--591. (English. English summary)
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