Melenk, J. M., & Rieder, A. (2022). An exponentially convergent discretization for space–time fractional parabolic equations using 𝘩𝘱-FEM. IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/drac045
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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Project title:
Numerische Methoden Höherer Ordnung für nichtlokale Operatoren: F 6507-N36 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
