Convergence of relaxation schemes to the equations of elastodynamics

Gosse, Laurent; Tzavaras, Athanasios

doi:10.1090/S0025-5718-00-01256-4

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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