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Mathematics > Numerical Analysis

Title: A-posteriori error estimates for systems of hyperbolic conservation laws

Authors: Jan Giesselmann, Aleksey Sikstel
(Submitted on 2 May 2023)
Abstract: We provide rigorous and computable 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 and a novel method to compute negative order norms of residuals. Numerical experiments show that the error estimator converges with the rate predicted by a-priori error estimates.
Subjects: Numerical Analysis (math.NA)
MSC classes: 35L40, 65M08, 65M15
Cite as: arXiv:2305.01340 [math.NA]
  (or arXiv:2305.01340v1 [math.NA] for this version)

Submission history

From: Aleksey Sikstel [view email]
[v1] Tue, 2 May 2023 11:38:42 GMT (3637kb,D)
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