TY - JOUR
T1 - A Posteriori Error Estimates for Numerical Solutions to Hyperbolic Conservation Laws
AU - Bressan, Alberto
AU - Chiri, Maria Teresa
AU - Shen, Wen
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.
PY - 2021/7
Y1 - 2021/7
N2 - This paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for n× n hyperbolic conservation laws in one space dimension. These estimates are achieved by a “post-processing algorithm”, checking that the numerical solution retains small total variation, and computing its oscillation on suitable subdomains. The results apply, in particular, to solutions obtained by the Godunov or the Lax–Friedrichs scheme, backward Euler approximations, and the method of periodic smoothing. Some numerical implementations are presented.
AB - This paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for n× n hyperbolic conservation laws in one space dimension. These estimates are achieved by a “post-processing algorithm”, checking that the numerical solution retains small total variation, and computing its oscillation on suitable subdomains. The results apply, in particular, to solutions obtained by the Godunov or the Lax–Friedrichs scheme, backward Euler approximations, and the method of periodic smoothing. Some numerical implementations are presented.
UR - http://www.scopus.com/inward/record.url?scp=85104115591&partnerID=8YFLogxK
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U2 - 10.1007/s00205-021-01653-4
DO - 10.1007/s00205-021-01653-4
M3 - Article
AN - SCOPUS:85104115591
SN - 0003-9527
VL - 241
SP - 357
EP - 402
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 1
ER -