Convergence Rates of Monotone Schemes for Conservation Laws for Data with Unbounded Total Variation

摘要

Abstract We prove convergence rates of monotone schemes for conservation laws for H?lder continuous initial data with unbounded total variation, provided that the H?lder exponent of the initial data is greater than 12documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$nicefrac {1}{2}$$end{document}. For strictly Lip+documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${{,mathrm{Lip},}}^+$$end{document} stable monotone schemes, we prove convergence for any positive H?lder exponent. Numerical experiments are presented which verify the theory.