  This study presents a new mass-lumping finite element method for computing
the radially symmetric solution of a semilinear heat equation in an $N$
dimensional ball ($N\ge 2$). We provide two schemes, (ML-1) and (ML-2), and
derive their error estimates through the discrete maximum principle. In the
weighted $L^{2}$ norm, the convergence of (ML-1) was at the optimal order but
that of (ML-2) was only at sub-optimal order. Nevertheless, scheme (ML-2)
reproduces a blow-up of the solution of the original equation. In fact, in
scheme (ML-2), we could accurately approximate the blow-up time. Our
theoretical results were validated in numerical experiments.
