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.

翻译：我们针对二维或三维空间中抛物-椭圆型Keller-Segel系统的间断Galerkin格式，提供了后验误差估计。该估计是条件性的——即要求某个后验可计算量足够小（可通过网格细化保证），并且是最优的——即误差估计量在网格细化下与误差具有相同的衰减阶数。我们误差估计量的一个显著特征是：基于数值结果，它可用于证明直至特定时刻的弱解存在性。