An L1-error bound for a semi-implicit difference scheme applied to a stiff system of conservation laws
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1224336
- author
- Schroll, Achim LU ; Tveito, Aslak and Winther, Ragnar
- publishing date
- 1997
- 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
- Society for Industrial and Applied Mathematics
- 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
- 2016-04-01 16:53:32
- date last changed
- 2022-02-05 19:20:18
@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}}, keywords = {{GODUNOV; RELAXATION; NUMERICAL-METHODS; DYNAMIC COMBUSTION; nonequilibrium; relaxation term; stiff hyperbolic conservation law; error estimate; MODEL}}, language = {{eng}}, number = {{3}}, pages = {{1152--1166}}, publisher = {{Society for Industrial and Applied Mathematics}}, 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}}, doi = {{10.1137/S0036142994268855}}, volume = {{34}}, year = {{1997}}, }