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arXiv · 1404.0068

A PDE approach to space-time fractional parabolic problems

Ricardo H. Nochetto·Enrique Otarola·Abner J. Salgado
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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.

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Ricardo H. Nochetto, Enrique Otarola, Abner J. Salgado. 2014-04-01. A PDE approach to space-time fractional parabolic problems. https://arxiv.org/abs/1404.0068

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