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J. Melenk, A. Rieder:
"hp-FEM for the fractional heat equation";
in: "ASC Report 12/2019", herausgegeben von: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2019, ISBN: 978-3-902627-12-4, S. 1 - 39.

We consider a time dependent problem generated by a nonlocal operator in space.
Applying a discretization scheme based on hp-Finite Elements and a Caffarelli-Silvestre extension we obtain a semidiscrete semigroup. The discretization in time is carried out by using hp-Discontinuous Galerkin based timestepping. We prove exponential convergence for such a method in an abstract framework for the discretization in the original domain.

http://www.asc.tuwien.ac.at/preprint/2019/asc12x2019.pdf