Preprint 2001-024
Error Bounds for the Large Time Step Glimm Scheme Applied to
Scalar Conservation Laws
J. Huang, J. Wang, and G. Warnecke
Abstract:
In this paper we derive an L1 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 x1/2|log \Delta x|)
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.
- Paper:
- Available as PostScript (536 Kbytes) or
gzipped PostScript (109 Kbytes; uncompress
using gunzip).
- Author(s):
- J. Huang
- J. Wang,
<jwang@iss06.iss.ac.cn>
- G. Warnecke,
<gerald.warnecke@mathematik.uni-magdeburg.de>
- Publishing information:
-
- Comments:
-
- Submitted by:
-
<gerald.warnecke@mathematik.uni-magdeburg.de>
July 10 2001.
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Last modified: Wed Jul 4 22:21:28 MET DST 2001