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- Title
An exponentially convergent discretization for space–time fractional parabolic equations using hp-FEM.
- Authors
Melenk, Jens Markus; Rieder, Alexander
- 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
SPACETIME; BOUNDARY value problems; INITIAL value problems; GALERKIN methods; EQUATIONS; QUADRATURE domains
- Publication
IMA Journal of Numerical Analysis, 2023, Vol 43, Issue 4, p2352
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/drac045