AN ADAPTIVE VERSION OF GLIMM'S SCHEME

doi:10.1016/S0252-9602(10)60057-4

Abstract

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 L¹(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.

Key words: conservation laws, finite difference methods, adaptive, error estimation, a-posteriori

CLC Number:

65M06

H. Kim, M. Laforest, D. Yoon. AN ADAPTIVE VERSION OF GLIMM'S SCHEME[J].Acta mathematica scientia,Series B, 2010, 30(2): 428-446.

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