%0 Journal Article
%T A PDE approach to space-time fractional parabolic problems
%A Ricardo H. Nochetto
%A Enrique Otarola
%A Abner J. Salgado
%J Mathematics
%D 2014
%I arXiv
%X We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem posed on a semi-infinite cylinder in one more spatial dimension. We write our evolution problem as a quasi-stationary elliptic problem with a dynamic boundary condition. We propose and analyze an implicit fully-discrete scheme: first-degree tensor product finite elements in space and an implicit finite difference discretization in time. We prove stability and error estimates for this scheme.
%U http://arxiv.org/abs/1404.0068v3