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Mathematics > Numerical Analysis

arXiv:1803.05212 (math)
[Submitted on 14 Mar 2018 (v1), last revised 29 Oct 2018 (this version, v2)]

Title:Maximum principle satisfying CWENO schemes for non-local conservation laws

Authors:Jan Friedrich, Oliver Kolb
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Abstract:Central WENO schemes are a natural candidate for higher-order schemes for non-local conservation laws, since the underlying reconstructions do not only provide single point values of the solution but a complete (high-order) reconstruction in every time step, which is beneficial to evaluate the integral terms. Recently, in [C. Chalons et al., SIAM J. Sci. Comput., 40(1), A288-A305], Discontinuous Galerkin (DG) schemes and Finite Volume WENO (FV-WENO) schemes have been proposed to obtain high-order approximations for a certain class of non-local conservation laws. In contrast to their schemes, the presented CWENO approach neither requires a very restrictive CFL condition (as the DG methods) nor an additional reconstruction step (as the FV-WENO schemes). Further, by making use of the well-known linear scaling limiter of [X. Zhang and C.-W. Shu, J. Comput. Phys., 229, p. 3091-3120], our CWENO schemes satisfy a maximum principle for suitable non-local conservation laws.
Subjects: Numerical Analysis (math.NA)
MSC classes: 65M08, 65M12
Cite as: arXiv:1803.05212 [math.NA]
  (or arXiv:1803.05212v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1803.05212
Journal reference: SIAM J. Sci. Comput., 41(2), A973-A988, 2019
Related DOI: https://doi.org/10.1137/18M1175586

Submission history

From: Oliver Kolb [view email]
[v1] Wed, 14 Mar 2018 11:39:20 UTC (363 KB)
[v2] Mon, 29 Oct 2018 20:30:57 UTC (31 KB)
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