The convergence rate of finite difference schemes in the presence of shocks
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
: 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.
finite difference approximation; shock wave; hyperbolic system
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-90359DOI: 10.1137/S0036142997317584OAI: oai:DiVA.org:kth-90359DiVA: diva2:505027
NR 201408052012-02-222012-02-22Bibliographically approved