l
1-error estimates on the immersed interface upwind scheme for linear convection equations with piecewise constant coefficients: A simple proof |
| |
Authors: | Shi Jin Peng Qi |
| |
Institution: | 1. Department of Mathematics, Institute of Natural Sciences and MOE Key Lab in Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai, 200240, China 2. Department of Mathematics, University of Wisconsin-Madison, Madison, WI, 53706, USA
|
| |
Abstract: | A linear convection equation with discontinuous coefficients arises in wave propagation through interfaces. An interface condition is needed at the interface to select a unique solution. An upwind scheme that builds this interface condition into its numerical flux is called the immersed interface upwind scheme. An l1-error estimate of such a scheme was first established by Wen et al. (2008). In this paper, we provide a simple analysis on the l 1-error estimate. The main idea is to formulate the solution to the underline initial-value problem into the sum of solutions to two convection equations with constant coefficients, which can then be estimated using classical methods for the initial or boundary value problems. |
| |
Keywords: | |
本文献已被 CNKI SpringerLink 等数据库收录! |
|