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Mathematics > Numerical Analysis

arXiv:2202.02067 (math)
[Submitted on 4 Feb 2022 (v1), last revised 10 Oct 2022 (this version, v2)]

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

Authors: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.
Subjects: Numerical Analysis (math.NA)
MSC classes: 65M60, 65M12, 65M15
Cite as: arXiv:2202.02067 [math.NA]
  (or arXiv:2202.02067v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2202.02067
Journal reference: IMA J. Numer. Anal. 43 (2023), pp. 2352--2376
Related DOI: https://doi.org/10.1093/imanum/drac045

Submission history

From: Alexander Rieder [view email]
[v1] Fri, 4 Feb 2022 10:40:13 UTC (314 KB)
[v2] Mon, 10 Oct 2022 13:34:50 UTC (370 KB)
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