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的抛物-椭圆型Keller-Segel系统，提出了不连续Galerkin格式的后验误差估计。该估计是条件性的，即后验可计算量需足够小（可通过网格细化来保证），且具有最优性，即误差估计子在网格细化下与误差以相同阶数衰减。我们误差估计子的一个显著特征在于，它能基于数值结果证明弱解在特定时间范围内的存在性。