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This paper concerns the study of the numerical approximation for the following boundary value problem:

where  is a  convex, nondecreasing function,  is symmetric for  The potential   We find some conditions under which the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its semidiscrete quenching time. We also prove that the semidiscrete quenching time converges to the real one when the mesh size goes to zero. A similar study has been also investigated taking a discrete form of the above problem. Finally, we give some numerical experiments to illustrate our analysis.

semidiscretizations, semilinear parabolic equation, quenching, numerical quenching time, convergence.