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

William McLean; Kassem Mustapha

doi:10.1007/s11075-021-01160-3

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

William McLean^*, Kassem Mustapha

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 language	English
Pages (from-to)	1441-1463
Number of pages	23
Journal	Numerical Algorithms
Volume	89
Issue number	4
DOIs	https://doi.org/10.1007/s11075-021-01160-3
State	Published - Apr 2022

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

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

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1007/s11075-021-01160-3

Cite this

@article{808fca0ae15f4ffc85f01f29eb7242d0,

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

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.",

keywords = "Discontinuous Galerkin method, Finite element method, Fractional calculus, Ritz projector, Stability analysis",

author = "William McLean and Kassem Mustapha",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2022",

month = apr,

doi = "10.1007/s11075-021-01160-3",

language = "English",

volume = "89",

pages = "1441--1463",

journal = "Numerical Algorithms",

issn = "1017-1398",

number = "4",

}

TY - JOUR

T1 - Uniform stability for a spatially discrete, subdiffusive Fokker–Planck equation

AU - McLean, William

AU - Mustapha, Kassem

PY - 2022/4

Y1 - 2022/4

N2 - 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.

AB - 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.

KW - Discontinuous Galerkin method

KW - Finite element method

KW - Fractional calculus

KW - Ritz projector

KW - Stability analysis

UR - https://www.scopus.com/pages/publications/85109939546

U2 - 10.1007/s11075-021-01160-3

DO - 10.1007/s11075-021-01160-3

M3 - Article

AN - SCOPUS:85109939546

SN - 1017-1398

VL - 89

SP - 1441

EP - 1463

JO - Numerical Algorithms

JF - Numerical Algorithms

IS - 4

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this