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This paper deals with a nonlinear parabolic equation for which a local solution in time exists and then blows up in a finite time. We consider the Chipot-Weissler equation: We study the numerical approximation, we show that the numerical solution converges to the continuous one under some restriction on the initial data and the parameters p and q. Moreover, we study the numerical blow up sets and we show that although the convergence of the numerical solution is guaranteed, the numerical blowdoi:10.3934/dcdss.2016057 fatcat:5gfjrkaur5h4towia65hqo54ea