TY - JOUR
T1 - Convergence of an Immersed Interface Upwind Scheme for Linear Advection Equations with Piecewise Constant Coefficients II: Some Related Binomial Coefficients Inequalities
AU - Xin Wen
JO - Journal of Computational Mathematics
VL - 4
SP - 474
EP - 483
PY - 2009
DA - 2009/08
SN - 27
DO - http://doi.org/10.4208/jcm.2009.27.4.014
UR - https://global-sci.org/intro/article_detail/jcm/8584.html
KW - Binomial coefficient, Linear advection equations, Immersed interface upwind
scheme, Piecewise constant coefficients, Error estimates.
AB - <p style="text-align: justify;">In this paper we give proof of three binomial coefficient inequalities. These inequalities are key ingredients in [Wen and Jin, J. Comput. Math. 26, (2008), 1-22] to establish the $L^1$-error estimates for the upwind difference scheme to the linear advection equations with a piecewise constant wave speed and a general interface condition, which were further used to establish the $L^1$-error estimates for a Hamiltonian-preserving scheme developed in [Jin and Wen, Commun. Math. Sci. 3, (2005), 285-315] to the Liouville equation with piecewise constant potentials [Wen and Jin, SIAM J. Numer. Anal. 46, (2008), 2688-2714].</p>