[2402.02295] WENO reconstructions of unconditionally optimal high order
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Mathematics > Numerical Analysis

arXiv:2402.02295 (math)
[Submitted on 3 Feb 2024]

Title:WENO reconstructions of unconditionally optimal high order

Authors:Antonio Baeza, Raimund Bürger, Pep Mulet, David Zorío
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Abstract:A modified Weighted Essentially Non-Oscillatory (WENO) reconstruction technique preventing accuracy loss near critical points (regardless of their order) of the underlying data is presented. This approach only uses local data from the reconstruction stencil and does not rely on any sort of scaling parameters. The key novel ingredient is a weight design based on a new smoothness indicator, which defines the first WENO reconstruction procedure that never loses accuracy on smooth data, regardless of the presence of critical points of any order, and is therefore addressed as optimal WENO (OWENO) method. The corresponding weights are non-dimensional and scale-independent. The weight designs are supported by theoretical results concerning the accuracy of the smoothness indicators. The method is validated by numerical tests related to algebraic equations, scalar conservation laws, and systems of conservation laws.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2402.02295 [math.NA]
  (or arXiv:2402.02295v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2402.02295
Journal reference: SIAM J. NUMER. ANAL. Vol. 57, No. 6, pp. 2760-2784 (2019)
Related DOI: https://doi.org/10.1137/18M1229900

Submission history

From: Antonio Baeza [view email]
[v1] Sat, 3 Feb 2024 23:17:18 UTC (456 KB)
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