TY - INPR A1 - Giesselmann, Jan A1 - Kolbe, Niklas T1 - A posteriori error analysis of a positivity preserving scheme for the power-law diffusion Keller-Segel model N2 - We study a finite volume scheme approximating a parabolic-elliptic Keller-Segel system with power law diffusion with exponent γ∈[1,3] and periodic boundary conditions. We derive conditional a posteriori bounds for the error measured in the L∞(0,T;H1(Ω)) norm for the chemoattractant and by a quasi-norm-like quantity for the density. These results are based on stability estimates and suitable conforming reconstructions of the numerical solution. We perform numerical experiments showing that our error bounds are linear in mesh width and elucidating the behaviour of the error estimator under changes of γ. KW - Keller-Segel KW - chemotaxis; KW - nonlinear diffusion KW - finite volume scheme KW - a posteriori error analysis Y1 - 2023 ER - TY - INPR A1 - Giesselmann, Jan A1 - Kwon, Kiwoong T1 - A posteriori error control for a Discontinuous Galerkin approximation of a Keller-Segel model N2 - 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. KW - Keller-Segel KW - chemotaxis KW - nonlinear diffusion KW - discontinuous Galerkin scheme KW - a posteriori error analysis Y1 - 2023 ER -