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

Jens Markus Melenk; Alexander Rieder

doi:10.1093/imanum/drac045

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

Numerical Analysis 2024-07-25 v2 Numerical Analysis

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.

Keywords

space-time fractional parabolic equations hp-fem sinc-quadrature riesz-dunford integral exponential convergence startup singularities

Cite

@article{arxiv.2202.02067,
  title  = {An exponentially convergent discretization for space-time fractional parabolic equations using $hp$-FEM},
  author = {Jens Markus Melenk and Alexander Rieder},
  journal= {arXiv preprint arXiv:2202.02067},
  year   = {2024}
}

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