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This paper concerns the study of the numerical approximation for the following parabolic equations with a nonlinear convection term    ut(x, t) = uxx(x, t) − u (x, t)ux(x, t) + u (x, t), 0 < x < 1, t > 0, ux(0, t) = 0, ux(1, t) = 0, t > 0, u(x, 0) = u0(x) > 0, 0 ≤ x ≤ 1, where q ≥ 1 and p ≥ q + 1. We find some conditions under which the solution of the discrete form of the above problem blows up in a finite time and estimate its numerical blow-up time. We also prove that the numerical blow-up time converges to the real one, when the mesh size goes to zero. Finally, we give some numerical experiments to illustrate ours analysis. AMS Subject Classification: 35K58, 35B44, 35B50, 35B51, 65M06, 35K28

BLOW-UP FOR DISCRETIZATIONS OF SOME REACTION-DIFFUSION EQUATIONS WITH A NONLINEAR CONVECTION TERM