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AN ADAPTIVE VERSION OF GLIMM'S SCHEME Dedicated to Professor James Glimm on the occasion of his 75th birthday

Authors
Kim, H.Laforest, M.Yoon, D.
Issue Date
Mar-2010
Publisher
SPRINGER
Keywords
conservation laws; finite difference methods; adaptive; error estimation; a- posteriori
Citation
ACTA MATHEMATICA SCIENTIA, v.30, no.2, pp.428 - 446
Indexed
SCIE
SCOPUS
Journal Title
ACTA MATHEMATICA SCIENTIA
Volume
30
Number
2
Start Page
428
End Page
446
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/116939
DOI
10.1016/S0252-9602(10)60057-4
ISSN
0252-9602
Abstract
This article describes a local error estimator for Glimm's scheme for hyperbolic systems of conservation laws and uses it to replace the usual random choice in Glimm's scheme by an optimal choice. As a by-product of the local error estimator, the procedure provides a global error estimator that is shown numerically to be a very accurate estimate of the error in L-1(R) for all times. Although there is partial mathematical evidence for the error estimator proposed, at this stage the error estimator must be considered ad-hoc. Nonetheless, the error estimator is simple to compute, relatively inexpensive, without adjustable parameters and at least as accurate as other existing error estimators. Numerical experiments in 1-D for Burgers' equation and for Euler's system are performed to measure the asymptotic accuracy of the resulting scheme and of the error estimator.
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