CONICET | Buscador de Institutos y Recursos Humanos

We propose a numerical method to approximate the solutionof a nonlocal diffusion problem on a general setting of metric measure spaces.These spaces include, but are not limited to, fractals, manifolds and Euclidean domains. We obtain error estimates in $L^infty(L^p)$ for $p=1,infty$ under the sole assumption of the initial datum being in $L^p$.An improved bound for the error in $L^infty(L^1)$ is obtained when the initial datum is in $L^2$.We also derive some qualitative properties of the solutions like stability,comparison principles and study the asymptotic behavior as $toinfty$.We finally present two examples on fractals: the Sierpinski gasket and the Sierpinski carpet, which illustrate on the effect of nonlocal diffusion for piecewise constant initial datum.