@Article{JCM-26-1,
author = {Xin Wen and Shi Jin},
title = {Convergence of an Immersed Interface Upwind Scheme for Linear Advection Equations with Piecewise Constant Coefficients I: $L^1$-Error Estimates},
journal = {Journal of Computational Mathematics},
year = {2008},
volume = {26},
number = {1},
pages = {1--22},
abstract = {<p style="text-align: justify;">We study the $L^1$-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 $L^1$-norm to the differential equation with the corresponding interface condition. We derive the one-halfth order $L^1$-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].</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/10363.html}
}