  In this paper, the authors propose a numerical method to compute the solution
of a nonlinear reaction-diffusion problem in the case of HS-regime. The initial
condition is a nonnegative function with compact support. The problem is split
in two parts: A hyperbolic term solved by using the Hopf and Lax formula and a
parabolic term solved by a backward linearized Euler method in time and a
finite element method in space. Estimates of the numerical solution are
obtained and it is proved that any numerical solution blows up in finite time.
