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

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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.

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Funding

The support of KFUPM through the project no. SB191003 is gratefully acknowledged.

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Authors and Affiliations

  1. School of Mathematics and Statistics, The University of New South Wales, Sydney, 2052, Australia

    William McLean

  2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Kassem Mustapha

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  1. William McLean
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  2. Kassem Mustapha
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Correspondence to William McLean.

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McLean, W., Mustapha, K. Uniform stability for a spatially discrete, subdiffusive Fokker–Planck equation. Numer Algor 89, 1441–1463 (2022). https://doi.org/10.1007/s11075-021-01160-3

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  • DOI: https://doi.org/10.1007/s11075-021-01160-3

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