A PDE approach to space-time fractional parabolic problems
Numerical Analysis
2015-03-05 v3
Abstract
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.
Cite
@article{arxiv.1404.0068,
title = {A PDE approach to space-time fractional parabolic problems},
author = {Ricardo H. Nochetto and Enrique Otarola and Abner J. Salgado},
journal= {arXiv preprint arXiv:1404.0068},
year = {2015}
}