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A posteriori error control for a Discontinuous Galerkin approximation of a Keller-Segel model

Submission Status:under review
  • We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional, in the sense that an a posteriori computable quantity needs to be small enough - which can be ensured by mesh refinement - and optimal in the sense that the error estimator decays with the same order as the error under mesh refinement. A specific feature of our error estimator is that it can be used to prove existence of a weak solution up to a certain time based on numerical results.

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Metadaten
Author:Jan Giesselmann, Kiwoong Kwon
Document Type:Preprint
Language:English
Date of Publication (online):2024/02/13
Release Date:2024/02/13
Tag:Keller-Segel; a posteriori error analysis; chemotaxis; discontinuous Galerkin scheme; nonlinear diffusion
Institutes:Technische Universität Darmstadt
Subprojects:C05
Licence (German):License LogoCreative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International