Total oscillation diminishing property for scalar conservation laws |
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Authors: | Benoît Perthame Michael Westdickenberg |
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Affiliation: | (1) Département de Mathématiques et Applications, École Normale Supérieure, CNRS UMR 8553, 45 rue dUlm, 75230 Paris cedex 05, France;(2) Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität Bonn, Wegelerstraße 10, 53115 Bonn |
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Abstract: | Summary. We prove a BV estimate for scalar conservation laws that generalizes the classical Total Variation Diminishing property. In fact, for any Lipschitz continuous monotone :, we have that |(u)|TV() is nonincreasing in time. We call this property Total Oscillation Diminishing because it is in contradiction with the oscillations observed recently in some numerical computations based on TVD schemes. We also show that semi-discrete Total Variation Diminishing finite volume schemes are TOD and that the fully discrete Godunov scheme is TOD.Mathematics Subject Classification (2000): 35L65, 35K55, 65M20 |
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