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We study the eect 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 Lp theory of compensated compactness. Then we study the convergence of an associated relaxation-diusion system, inspired by the scheme. Numerical comparisons of fully-discrete schemes are carried out.

Convergence of relaxation schemes to the equations of elastodynamics