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On the behavior of the total variation in CWENO methods for conservation laws

✍ Scribed by Doron Levy; Gabriella Puppo; Giovanni Russo

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
109 KB
Volume
33
Category
Article
ISSN
0168-9274

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✦ Synopsis

We consider a family of high-order, weighted essentially non-oscillatory central schemes (CWENO) for approximating solutions of one-dimensional hyperbolic systems of conservation laws. We are interested in the behavior of the total variation (TV) of the approximate solution obtained with these methods. Our numerical results suggest that even though CWENO methods are not total variation diminishing (TVD), they do have bounded total variation (TVB). Moreover, the TV of the approximate solution seems to never increase above the theoretical value, and it approaches it as the mesh is refined. These results are hopefully a first step in the quest for proving the convergence of such high-order methods.

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