The porous medium equation (PME) is a nonlinear degenerate equation with the finite speed and possible waiting time. Based on an energetic variational approach, a structure-preserving numerical scheme for the one-dimensional PME has been constructed in [12], which preserves the positivity of the solution and the mass conservation, the energy dissipation law, as well as an efficient calculation of the finite speed and the waiting time. In this paper, we use a similar approach to numerically solve a radially symmetric solution of PME in \(\mathbb {R}^d\) , \(d\ge 2\) . It is proved that the numerical scheme is uniquely solvable on an admissible convex set and satisfies the original discrete energy dissipation law. Moreover, the optimal rate convergence analysis and error estimate is theoretically established. The two and three dimensional simulation results indicate that the numerical method is effective in solving the axisymmetric solutions of the PME equation, and compute the finite speed and the waiting time effectively. As another advantage, we give the convergence order of the radially symmetric solution with a support and the waiting time numerically in two dimension.
