Numerical quenching for the semilinear heat equation with a singular absorption

In this paper we study the numerical approximation for the heat equation with a singular absorption. We prove that the numerical quenching rate coincides with the continuous one. We also see that the quenching time and the quenching set converge to the continuous one. In fact, under some restriction on the initial data, the numerical quenching coincides with the continuous one. Finally, we give some numerical results to illustrate our analysis.