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We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $partial_t u-mathfrak{L}[varphi(u)]=f(x,t)$ in $mathbb{R}^Ntimes(0,T),$ where $mathfrak{L}$ is a general symmetric Levy-type diffusion operator. Included are both local and nonlocal problems with, e.g., $mathfrak{L}=Delta$ or $mathfrak{L}=-(-Delta)^{fracalpha2}$, $alphain(0,2)$, and porous medium, fast diffusion, and Stefan-type nonlinearities $varphi$. By robust methods we mean that they converge even for nonsmooth solutions and under very weak assumptions on the data. We show that they are $L^p$-stable for $pin[1,infty]$, compact, and convergent in $C([0,T];L_{textup{loc}}^p(mathbb{R}^N))$ for $pin[1,infty)$. The first part of this project is given in [F. del Teso, J. Endal, and E. R. Jakobsen, preprint, arXiv:1801.07148v1 [math.NA], 2018] and contains the unified and easy to use theoretical framework. This paper is devoted to schemes and testi...

Robust Numerical Methods for Nonlocal (and Local) Equations of Porous Medium Type. Part II: Schemes and Experiments