An exponentially convergent discretization for space-time fractional parabolic equations using hp-FEM

02/04/2022

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by   Jens Markus Melenk, et al.

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We consider a space-time fractional parabolic problem. Combining a sinc-quadrature based method for discretizing the Riesz-Dunford integral with hp-FEM in space yields an exponentially convergent scheme for the initial boundary value problem with homogeneous right-hand side. For the inhomogeneous problem, an hp-quadrature scheme is implemented. We rigorously prove exponential convergence with focus on small times t, proving robustness with respect to startup singularities due to data incompatibilities.