Uniform stability for a spatially discrete, subdiffusive Fokker–Planck equation

William McLean, Kassem Mustapha

Research output: Contribution to journalJournal articlepeer-review

Abstract

We prove stability estimates for the spatially discrete, Galerkin solution of a fractional Fokker–Planck equation, improving on previous results in several respects. Our main goal is to establish that the stability constants are bounded uniformly in the fractional diffusion exponent α ∈ (0,1). In addition, we account for the presence of an inhomogeneous term and show a stability estimate for the gradient of the Galerkin solution. As a by-product, the proofs of error bounds for a standard finite element approximation are simplified.

Original languageEnglish
JournalNumerical Algorithms
DOIs
StateAccepted/In press - 2021

Keywords

  • Discontinuous Galerkin method
  • Finite element method
  • Fractional calculus
  • Ritz projector
  • Stability analysis

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