Convergence of an immersed interface upwind scheme for linear advection equations with piecewise constant coefficients I : L 1-error estimates

@inproceedings{Wen2007ConvergenceOA,
title={Convergence of an immersed interface upwind scheme for linear advection equations with piecewise constant coefficients I : L 1-error estimates},
author={Xin Wen and Shi Mei Jin Jin},
year={2007}
}

We study the L1-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 L1-norm to the differential equation with the corresponding interface condition. We derive the one-halfth order L1-error bounds… CONTINUE READING