propagation: if $u_0({\boldsymbol{x}})$ has a compact support, the solution will have a compact support for any time $t > t_0$. This in effect creates a free boundary that stays between the regions where $u$ is nonzero and where $u$ vanishes and propagates at a finite speed for all time. Contrary to the heat equation which smooths out its initial solutions, PME solution can become nonsmooth even in cases where it has a smooth initial solution. Moreover, for a certain type of initial solutions, the solution can exhibit a waiting-time phenomenon for which the free boundary will not move until a finite amount of time has elapsed. PME has been studied extensively in theory and there is a vast literature, including the earlier work by Ole[ĭ]{}nik et al. [@Oleinik1958], Kala[š]{}nikov [@Kalashnikov1967], Aronson [@Aronson1969], the more recent work by Shmarev [@Shmarev2005; @Shmarev2003], and the monograph by V[á]{}zquez [@Vazquez2007] and references therein.

The numerical solution of PME has also received considerable attention from researchers. Particularly, error estimates have been obtained for various finite element approximations. For example, using a regularization approach (to avoid degenerate or negative diffusion, for instance, with the diffusion coefficient $|u|^m$ being replaced by $\max (|u|, \epsilon/2)^m$ for some regularization 