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A Remark on Numerical Errors Downstream of Slightly Viscous Shocks
KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
1999 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 36, no 3, 853-863 p.Article in journal (Refereed) Published
##### Abstract [en]

Lower-order errors downstream of a shock layer have been detected in computations with nonconstant solutions when using higher-order shock capturing schemes in one and two dimensions [B. Engquist and B. Sjögreen, {SIAM J. Numer. Anal., 35 (1998), pp. 2464--2485].By analyzing the steady-state solution of slightly viscous hyperbolic systems of conservation laws we find that the solution can have an ${\cal O}(h)$-dependence downstream of a shock layer, although the viscous term in that region is of ${\cal O}(h^2)$. Numerical examples illustrate the analysis.

##### Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 1999. Vol. 36, no 3, 853-863 p.
Mathematics
##### Identifiers
OAI: oai:DiVA.org:kth-65749DiVA: diva2:483624
##### Note
NR 20140805Available from: 2012-01-25 Created: 2012-01-25Bibliographically approved

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##### By organisation
Numerical Analysis and Computer Science, NADA
##### In the same journal
SIAM Journal on Numerical Analysis
Mathematics