| CONVERGENCE OF AN IMMERSED INTERFACE UPWIND SCHEME FOR LINEAR ADVECTION EQUATIONS WITH PIECEWISE CONSTANT COEFFICIENTS I： L^1-ERROR ESTIMATES |
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| 基金项目： | Acknowledgments.This research is supported in part by the Knowledge Innovation Project of the Chinese Academy of Sciences Nos. K5501312S1 and K5502212F1, and NSFC grant No. 10601062. It is also supported in part by NSF grant Nos. DMS-0305081 and DMS-0608720, NSFC grant No. 10228101 and NSAF grant No. 10676017. We thank Prof. W.A. Yong, Dr. D. Yin and Mr. H. Wu for some fruitful discussions. |
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| 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].
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| 关 键 词： | 线性平流方程 分段常系数 误差估计 偏微分方程 |
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