the initial-boundary value problem (IBVP) of the porous medium equation (PME) in two dimensions, $$\begin{cases}
        u_t = \div(|u|^m \grad u) , \quad & \text{in} \quad \Omega \times (t_0,T]  \\
        u({\boldsymbol{x}},t_0) = u_0({\boldsymbol{x}}) , \quad & \text{on} \quad \Omega \\
        u({\boldsymbol{x}},t) = 0 , \quad & \text{on} \quad \p \Omega  \times (t_0,T]
    \end{cases}
  \label{PME-1}$$ where $\Omega$ is a bounded polygonal domain, $u_0({\boldsymbol{x}})$ is a given function, and $m\ge 1$ is a physical parameter. PME is a nontrivial generalization of the heat equation. It is found in many areas of the physical sciences, including gas flow in porous medium, incompressible fluid dynamics, nonlinear heat transfer, and image processing; e.g., see [@Vazquez2007] and references therein. In the case of gas flow in porous medium, $u$ represents the density of the gas, $u^m$ the pressure, $u \grad (u^m)$ the flux, $\grad (u^m)$ the velocity, and $m$ is the isentropic coefficient. In the case of radiation diffusion in plasmas, $m$ stands for the power of temperature appearing in the nonlinear diffusion coefficient and can take values up to 5.5 [@Vazquez2007 Page 23]. PME itself represents a nonlinear diffusion process. One of its many interesting features is its degeneracy which induces a property of the finite 