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The Keller-Segel equations are widely used for describing chemotaxis inbiology. Recently, a new fully discrete scheme for this model was proposed in[46], mass conservation, positivity and energy decay were proved for theproposed scheme, which are important properties of the original system. In thispaper, we establish the error estimates of this scheme. Then, based on theerror estimates, we derive the finite-time blowup of nonradial numericalsolutions under some conditions on the mass and the moment of the initial data.

Error estimates and blow-up analysis of a finite-element approximation for the parabolic-elliptic Keller-Segel system