Affiliation:
1. Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA
Abstract
In this study, we use an extension of Yang’s convergence criterion [N. Jiang, On the wavewise entropy inequality for high-resolution schemes with source terms II: the fully discrete case] to show the entropy convergence of a class of fully discrete α schemes, now with source terms, for non-homogeneous scalar convex conservation laws in the one-dimensional case. The homogeneous counterparts (HCPs) of these schemes were constructed by S. Osher and S. Chakravarthy in the mid-1980s [A New Class of High Accuracy TVD Schemes for Hyperbolic Conservation Laws (1985), Very High Order Accurate TVD Schemes (1986)], and the entropy convergence of these methods, when m=2, was settled by the author [N. Jiang, The Convergence of α Schemes for Conservation Laws II: Fully-Discrete]. For semi-discrete α schemes, with or without source terms, the entropy convergence of these schemes was previously established (for m=2) by the author [N. Jiang, The Convergence of α Schemes for Conservation Laws I: Semi-Discrete Case].
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference19 articles.
1. Chakravarthy, S., and Osher, S. (1985, January 14–17). A New Class of High Accuracy TVD Schemes for Hyperbolic Conservation Laws. Proceedings of the 23rd Aerospace Science Meeting, Reno, NV, USA.
2. Very High Order Accurate TVD Schemes;Osher;J. Oscil. Theory Comput. Methods Compens. Compact.,1986
3. Chakravarthy, S., and Osher, S. (1983, January 5–11). Computing with High Resolution Upwind Schemes for Hyperbolic Equations. Proceedings of the AMS-SIAM 1983, Boulder, CO, USA.
4. The Convergence of α Schemes for Conservation Laws II: Fully-Discrete Case;Jiang;Methods Appl. Anal.,2014
5. On the wavewise entropy inequality for high-resolution schemes with source terms II: The fully discrete case;Jiang;Methods Appl. Anal.,2019