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

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—...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 50; no. 6
Main Authors Giesselmann, Jan, Kwon, Kiwoong
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.12.2024
Subjects
Estimates
Galerkin method
Grid refinement (mathematics)
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Summary: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 the existence of a weak solution up to a certain time based on numerical results.
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-024-10212-w