CONVERGENCE OF AN IMMERSED INTERFACE UPWIND SCHEME FOR LINEAR ADVECTION EQUATIONS WITH PIECEWISE CONSTANT COEFFICIENTS Ⅱ: SOME RELATED BINOMIAL COEFFICIENT INEQUALITIES

• 来源期刊: 计算数学（英文版）
• 关键词: Binomial coefficient Linear advection equations Immersed interface upwind scheme Piecewise constant coefficients Error estimates
• 年，卷（期）: 2009,（4）
• 页码范围: 474-483
• 页数: 10页
• 语种: 英文
• DOI: 10.4208/jcm.2009.27.4.014

摘要

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 L1-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 L1-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].