Two computable conditional a posteriori error estimators for a Keller-Segel FV-FE scheme are proven, and satisfaction of their conditions certifies existence of a weak solution up to time T.
Bartels.Numerical methods for partial differential equations
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A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme
Two computable conditional a posteriori error estimators for a Keller-Segel FV-FE scheme are proven, and satisfaction of their conditions certifies existence of a weak solution up to time T.