A-posteriori error estimates for systems of hyperbolic conservation laws via computing negative norms of local residuals

IF 2.3 2区 数学 Q1 MATHEMATICS, APPLIED IMA Journal of Numerical Analysis Pub Date : 2025-03-11 DOI:10.1093/imanum/drae111
Jan Giesselmann, Aleksey Sikstel
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Abstract

We prove rigorous a-posteriori error estimates for first-order finite-volume approximations of nonlinear systems of hyperbolic conservation laws in one spatial dimension. Our estimators rely on recent stability results by Bressan, Chiri and Shen, a new way to localize residuals and a novel method to compute negative-order norms of these local residuals. Computing negative-order norms becomes possible by suitably projecting test functions onto a finite dimensional space. Numerical experiments show that the error estimator converges with the rate predicted by a-priori error estimates.
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来源期刊
IMA Journal of Numerical Analysis
IMA Journal of Numerical Analysis 数学-应用数学
CiteScore
5.30
自引率
4.80%
发文量
79
审稿时长
6-12 weeks
期刊介绍: The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects. Occasional survey articles are also published.
期刊最新文献
Numerical schemes for radial Dunkl processes Well-posedness of first-order acoustic wave equations and space-time finite element approximation A-posteriori error estimates for systems of hyperbolic conservation laws via computing negative norms of local residuals A noncoforming virtual element approximation for the Oseen eigenvalue problem Analysis and finite element approximation of a diffuse interface approach to the Stokes–Biot coupling
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