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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