Finite volume relaxation schemes for multidimensional conservation laws

Katsaounis, Theodoros; Makridakis, Charalambos

doi:10.1090/S0025-5718-00-01188-1

Finite volume relaxation schemes for multidimensional conservation laws
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by Theodoros Katsaounis and Charalambos Makridakis PDF

Math. Comp. 70 (2001), 533-553 Request permission

Abstract:

We consider finite volume relaxation schemes for multidimensional scalar conservation laws. These schemes are constructed by appropriate discretization of a relaxation system and it is shown to converge to the entropy solution of the conservation law with a rate of $h^{1/4}$ in $L^{\infty }([0, T] , L^{1} _\mathrm {loc}({\mathbb {R}} ^{d} ))$.

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