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On the Rate of Convergence of Viscosity Solutions for Boundary Value Problems

Lorenz, Jens and Sanders, Richard (1987) On the Rate of Convergence of Viscosity Solutions for Boundary Value Problems. SIAM Journal of Mathematical Analysis, 18 (2). pp. 306-320. ISSN 0036-1410. http://resolver.caltech.edu/CaltechAUTHORS:LORsiamjma87

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Abstract

A class of singularly perturbed boundary value problems is considered for viscosity tending to zero. From compactness arguments it is known that the solutions converge to a limit function characterized by an entropy inequality. We formulate an approximate entropy inequality (AEI) and use it to obtain the order of convergence. The AEI is also used to obtain the order of convergence for monotone difference schemes.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/0518024DOIUNSPECIFIED
Additional Information:© 1987 Society for Industrial and Applied Mathematics. Received by the editors January 13, 1986; accepted for publication May 8, 1986. The research of this author [J.L.] was supported by National Science Foundation grant DMS 83-12264 and Department of Energy grant DE/AT/03/76ER/72012. The research of this author [R.S.] was supported by National Science Foundation grant DMS 8505422.
Funders:
Funding AgencyGrant Number
Department of EnergyDE/AT/03/76ER/72012
National Science FoundationDMS 8505422
Subject Keywords:singular perturbations, entropy inequality, bounded variation functions
Record Number:CaltechAUTHORS:LORsiamjma87
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:LORsiamjma87
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12047
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:21 Oct 2008 06:42
Last Modified:26 Dec 2012 10:26

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