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An L1-error bound for a semi-implicit difference scheme applied to a stiff system of conservation laws

Schroll, Achim LU ; Tveito, Aslak and Winther, Ragnar (1997) In SIAM Journal on Numerical Analysis 34(3). p.1152-1166
Abstract
A straightforward semi-implicit finite-difference method approximating a system of conservation laws including a stiff relaxation term is analyzed. We show that the error, measured in L-1, is bounded by O(root Delta t) independent of the stiffness, where the time step Delta t represents the mesh size. As a simple corollary we obtain that solutions of the stiff system converge toward the solution of an equilibrium model at a rate of O(delta(1/3)) in L-1 as the relaxation time delta tends to zero.
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
GODUNOV, RELAXATION, NUMERICAL-METHODS, DYNAMIC COMBUSTION, nonequilibrium, relaxation term, stiff hyperbolic conservation law, error estimate, MODEL
in
SIAM Journal on Numerical Analysis
volume
34
issue
3
pages
1152 - 1166
publisher
SIAM Publications
external identifiers
  • scopus:0039026206
ISSN
0036-1429
DOI
10.1137/S0036142994268855
language
English
LU publication?
no
id
897046ae-68b8-4485-a8c6-69eb1a8c18ed (old id 1224336)
alternative location
http://www.jstor.org/sici?sici=0036-1429(199706)34%3A3%3C1152%3AALBFAS%3E2.0.CO%3B2-K&origin=ISI
date added to LUP
2008-09-02 11:55:02
date last changed
2017-02-26 04:17:58
@article{897046ae-68b8-4485-a8c6-69eb1a8c18ed,
  abstract     = {A straightforward semi-implicit finite-difference method approximating a system of conservation laws including a stiff relaxation term is analyzed. We show that the error, measured in L-1, is bounded by O(root Delta t) independent of the stiffness, where the time step Delta t represents the mesh size. As a simple corollary we obtain that solutions of the stiff system converge toward the solution of an equilibrium model at a rate of O(delta(1/3)) in L-1 as the relaxation time delta tends to zero.},
  author       = {Schroll, Achim and Tveito, Aslak and Winther, Ragnar},
  issn         = {0036-1429},
  keyword      = {GODUNOV,RELAXATION,NUMERICAL-METHODS,DYNAMIC COMBUSTION,nonequilibrium,relaxation term,stiff hyperbolic conservation law,error estimate,MODEL},
  language     = {eng},
  number       = {3},
  pages        = {1152--1166},
  publisher    = {SIAM Publications},
  series       = {SIAM Journal on Numerical Analysis},
  title        = {An L1-error bound for a semi-implicit difference scheme applied to a stiff system of conservation laws},
  url          = {http://dx.doi.org/10.1137/S0036142994268855},
  volume       = {34},
  year         = {1997},
}