TY - JOUR
T1 - On the Convergence of β-Schemes
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 - <p style="text-align: justify;">Yang&#39;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.</p>