CONVERGENCE OF AN IMMERSED INTERFACE UPWIND SCHEME FOR LINEAR ADVECTION EQUATIONS WITH PIECEWISE CONSTANT COEFFICIENTS I:L^1-ERROR ESTIMATES

作     者：Xin Wen Shi Jin 

作者机构：LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Department of Mathematics University of Wisconsin Madison WI 53706 USAand Department of Mathematical Sciences Tsinghua University Beijing 100084 China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2008年第26卷第1期

页      面：1-22页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported in part by the Knowledge Innovation Project of the Chinese Academy of Sciences Nos. K5501312S1 and K5502212F1, and NSFC grant No. 10601062 supported in part by NSF grant Nos. DMS-0305081 and DMS-0608720, NSFC grant No. 10228101 and NSAF grant No. 10676017 

主　　题：Linear advection equations Immersed interface upwind scheme Piecewise constant coefficients Error estimate Half order error bound 

摘      要：We study the L^l-error estimates for the upwind scheme to the linear advection equations with a piecewise constant coefficients modeling linear waves crossing interfaces. Here the interface condition is immersed into the upwind scheme. We prove that, for initial data with a bounded variation, the numerical solution of the immersed interface upwind scheme converges in L^l-norm to the differential equation with the corresponding interface condition. We derive the one-halfth order L^l-error bounds with explicit coefficients following a technique used in [25]. We also use some inequalities on binomial coefficients proved in a consecutive paper [32].