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The convergence rate of finite difference schemes in the presence of shocks
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
1998 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 35, no 6, 2464-2485 p.Article in journal (Refereed) Published
Abstract [en]

: Finite difference approximations generically have O(1) pointwise errors close to a shock. We show that this local error may effect the smooth part of the solution such that only first order is achieved even for formally higher-order methods. Analytic and numerical examples of this form of accuracy are given. We also show that a converging method will have the formal order of accuracy in domains where no characteristics have passed through a shock.

Place, publisher, year, edition, pages
1998. Vol. 35, no 6, 2464-2485 p.
Keyword [en]
finite difference approximation; shock wave; hyperbolic system
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-90359DOI: 10.1137/S0036142997317584OAI: diva2:505027
NR 20140805Available from: 2012-02-22 Created: 2012-02-22Bibliographically approved

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Engquist, Björn
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