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

초록

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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