TY - JOUR
T1 - Convergence of an Immersed Interface Upwind Scheme for Linear Advection Equations with Piecewise Constant Coefficients I: $L^1$-Error Estimates
AU - Xin Wen & Shi Jin
JO - Journal of Computational Mathematics
VL - 1
SP - 1
EP - 22
PY - 2008
DA - 2008/02
SN - 26
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/10363.html
KW - Linear advection equations, Immersed interface upwind scheme, Piecewise
constant coefficients, Error estimate, Half order error bound.
AB - <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>