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Error bounds for the large time step Glimm scheme applied to scalar conservation laws.
- Source :
- Numerische Mathematik; Mar2002, Vol. 91 Issue 1, p13-34, 22p
- Publication Year :
- 2002
-
Abstract
- In this paper we derive an $L^1$ error bound for the large time step, i.e. large Courant number, version of the Glimm scheme when used for the approximation of solutions to a genuinely nonlinear, i.e. convex, scalar conservation law for a generic class of piecewise constant data. We show that the error is bounded by $O(\Delta x^{1/2}\vert \log\Delta x\vert )$ for Courant numbers up to 1. The order of the error is the same as that given by Hoff and Smoller [5] in 1985 for the Glimm scheme under the restriction of Courant numbers up to 1/2. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0029599X
- Volume :
- 91
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Numerische Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 49989730
- Full Text :
- https://doi.org/10.1007/s002110100335