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Mathematics > Numerical Analysis

arXiv:1804.07796 (math)
[Submitted on 20 Apr 2018 (v1), last revised 14 Jan 2021 (this version, v3)]

Title:A second-order numerical method for the aggregation equations

Authors:José A. Carrillo, Ulrik Skre Fjordholm, Susanne Solem
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Abstract:Inspired by so-called TVD limiter-based second-order schemes for hyperbolic conservation laws, we develop a second-order accurate numerical method for multi-dimensional aggregation equations. The method allows for simulations to be continued after the first blow-up time of the solution. In the case of symmetric, lambda-convex potentials with a possible Lipschitz singularity at the origin we prove that the method converges in the Monge--Kantorovich distance towards the unique gradient flow solution. Several numerical experiments are presented to validate the second-order convergence rate and to explore the performance of the scheme.
Comments: Improved manuscript
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1804.07796 [math.NA]
  (or arXiv:1804.07796v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1804.07796

Submission history

From: Susanne Solem [view email]
[v1] Fri, 20 Apr 2018 18:55:43 UTC (1,512 KB)
[v2] Tue, 19 Nov 2019 11:28:29 UTC (1,586 KB)
[v3] Thu, 14 Jan 2021 12:38:16 UTC (1,587 KB)
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