Abstract
In this paper we address the questions of the convergence rate for approximate solutions to conservation laws with piecewise smooth solutions in a weighted W1,1 space. Convergence rate for the derivative of the approximate solutions is established under the assumption that a weak pointwise-error estimate is given. In other words, we are able to convert weak pointwise-error estimates to optimal error bounds in a weighted W1,1 space. For convex conservation laws, the assumption of a weak pointwise-error estimate is verified by Tadmor [ SIAM J. Numer. Anal., 28 (1991), pp. 891--906]. Therefore, one immediate application of our W1,1 - convergence theory is that for convex conservation laws we indeed have W1,1 -error bounds for the approximate solutions to conservation laws. Furthermore, the $\cO(\en)$-pointwise-error estimates of Tadmor and Tang [ SIAM J. Numer. Anal., 36 (1999), pp. 1739--1758] are recovered by the use of the W1,1 -convergence result.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
