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Finite volume relaxation schemes for multidimensional conservation laws |
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| Authors: | Theodoros Katsaounis Charalambos Makridakis |
| Institution: | Ecole Normale Supérieure, Département de Mathématique et d'Informatique, 45 rue d'Ulm, 75230 Paris Cedex 05, France ; Department of Mathematics, University of Crete, 714 09 Heraklion, Crete, and Institute of Applied and Computational Mathematics, FORTH, 711 10 Heraklion, Crete, Greece |
| 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  in ![$L^{\infty }(0, T] , L^{1} _\mathrm{loc}({\mathbb{R}} ^{d} ))\,$](http://www.ams.org/mcom/2001-70-234/S0025-5718-00-01188-1/gif-abstract0/img2.gif){kind=small} . |
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