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arXiv · 2202.02067

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

Jens Markus Melenk·Alexander Rieder
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Abstract

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.

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Jens Markus Melenk, Alexander Rieder. 2022-02-04. An exponentially convergent discretization for space-time fractional parabolic equations using $hp$-FEM. https://doi.org/10.1093/imanum%2Fdrac045

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