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. doi:10.1137/0518024. https://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 | ||||||
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| 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. | ||||||
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| Subject Keywords: | singular perturbations, entropy inequality, bounded variation functions | ||||||
| Issue or Number: | 2 | ||||||
| DOI: | 10.1137/0518024 | ||||||
| Record Number: | CaltechAUTHORS:LORsiamjma87 | ||||||
| Persistent URL: | https://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: | 08 Nov 2021 22:25 |
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