Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions

摘要

In this paper, we study the asymptotic behaviour of a semidiscrete numerical approximation for ut=uxx+up in a bounded interval, (0,1), with Dirichlet boundary conditions. We focus in the behaviour of blowing up solutions. We find that the blow-up rate for the numerical scheme is the same as for the continuous problem. Also we find the blow-up set for the numerical approximations and prove that it is contained in a neighbourhood of the blow-up set of the continuous problem when the mesh parameter is small enough.