Convergence of an Immersed Interface Upwind Scheme for Linear Advection Equations with Piecewise Constant Coefficients I: $L^1$-Error Estimates
Year: 2008
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 1 : pp. 1–22
Abstract
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].
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-JCM-10363
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 1 : pp. 1–22
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Linear advection equations Immersed interface upwind scheme Piecewise constant coefficients Error estimate Half order error bound.