Year: 2017
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 1 : pp. 103–125
Abstract
Yang's wavewise entropy inequality [19] is verified for $β$-schemes which, when $m = 2$ and under a mild technique condition, guarantees the convergence of the schemes to the entropy solutions of convex conservation laws in one-dimensional scalar case. These schemes, constructed by S. Osher and S. Chakravarthy [13], are based on unwinding principle and use E-schemes as building blocks with simple flux limiters, without which all of them are even linearly unstable. The total variation diminishing property of these methods was established in the original work of S. Osher and S. Chakravarthy.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2017-IJNAM-413
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 1 : pp. 103–125
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Conservation laws fully-discrete $β$-schemes entropy convergence.