<div class="csl-bib-body">
<div class="csl-entry">Melenk, J. M., & Rieder, A. (2022). An exponentially convergent discretization for space–time fractional parabolic equations using 𝘩𝘱-FEM. <i>IMA Journal of Numerical Analysis</i>. https://doi.org/10.1093/imanum/drac045</div>
</div>
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dc.identifier.issn
0272-4979
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/139352
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dc.description.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.
en
dc.description.sponsorship
Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.language.iso
en
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dc.publisher
OXFORD UNIV PRESS
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dc.relation.ispartof
IMA Journal of Numerical Analysis
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dc.subject
fractional diffusion
en
dc.subject
sinc quadrature
en
dc.subject
Mittag-Leffler
en
dc.subject
Riesz–Dunford
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dc.subject
𝘩𝘱-FEM
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dc.title
An exponentially convergent discretization for space–time fractional parabolic equations using 𝘩𝘱-FEM
en
dc.type
Article
en
dc.type
Artikel
de
dc.relation.grantno
F 6507-N36
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dc.type.category
Original Research Article
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tuw.journal.peerreviewed
true
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tuw.peerreviewed
true
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tuw.project.title
Numerische Methoden Höherer Ordnung für nichtlokale Operatoren