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Volume 14, Issue 1
On the Convergence of β-Schemes

N. Jiang

Int. J. Numer. Anal. Mod., 14 (2017), pp. 103-125.

Published online: 2016-01

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  • 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.

  • Keywords

Conservation laws, fully-discrete $β$-schemes, entropy convergence.

  • AMS Subject Headings

65M12, 35L60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-103, author = {N. Jiang}, title = {On the Convergence of β-Schemes}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {14}, number = {1}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/413.html} }
TY - JOUR T1 - On the Convergence of β-Schemes AU - N. Jiang JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 103 EP - 125 PY - 2016 DA - 2016/01 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/413.html KW - Conservation laws, fully-discrete $β$-schemes, entropy convergence. AB -

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.

N. Jiang. (2016). On the Convergence of β-Schemes. International Journal of Numerical Analysis and Modeling. 14 (1). 103-125. doi:
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