The finite volume element method for the two-dimensional space-fractional convection–diffusion equation

The finite volume element method for the two-dimensional space-fractional convection–diffusion equation

Abstract We develop a fully discrete finite volume element scheme of the two-dimensional space-fractional convection–diffusion equation using the finite volume element method to discretize the space-fractional derivative and Crank–Nicholson scheme for time discretization. We also analyze and prove t...

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Main Authors: Yanan Bi, Ziwen Jiang
Format: Article
Language:English
Published: SpringerOpen 2021-08-01
Series:Advances in Difference Equations
Subjects:
Fractional derivative
Finite volume element method
Stability
Convergence
Convection–diffusion equation
Online Access:https://doi.org/10.1186/s13662-021-03524-4
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spelling doaj-1e48f55a48334104843a0469e73c30d12021-08-22T11:12:02ZengSpringerOpenAdvances in Difference Equations1687-18472021-08-012021112210.1186/s13662-021-03524-4The finite volume element method for the two-dimensional space-fractional convection–diffusion equationYanan Bi0Ziwen Jiang1School of Mathematics and Statistics, Shandong Normal UniversitySchool of Mathematics and Statistics, Shandong Normal UniversityAbstract We develop a fully discrete finite volume element scheme of the two-dimensional space-fractional convection–diffusion equation using the finite volume element method to discretize the space-fractional derivative and Crank–Nicholson scheme for time discretization. We also analyze and prove the stability and convergence of the given scheme. Finally, we validate our theoretical analysis by data from three examples.https://doi.org/10.1186/s13662-021-03524-4Fractional derivativeFinite volume element methodStabilityConvergenceConvection–diffusion equation
collection DOAJ
language English
format Article
sources DOAJ
author Yanan Bi
Ziwen Jiang
spellingShingle Yanan Bi
Ziwen Jiang
The finite volume element method for the two-dimensional space-fractional convection–diffusion equation
Advances in Difference Equations
Fractional derivative
Finite volume element method
Stability
Convergence
Convection–diffusion equation
author_facet Yanan Bi
Ziwen Jiang
author_sort Yanan Bi
title The finite volume element method for the two-dimensional space-fractional convection–diffusion equation
title_short The finite volume element method for the two-dimensional space-fractional convection–diffusion equation
title_full The finite volume element method for the two-dimensional space-fractional convection–diffusion equation
title_fullStr The finite volume element method for the two-dimensional space-fractional convection–diffusion equation
title_full_unstemmed The finite volume element method for the two-dimensional space-fractional convection–diffusion equation
title_sort finite volume element method for the two-dimensional space-fractional convection–diffusion equation
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2021-08-01
description Abstract We develop a fully discrete finite volume element scheme of the two-dimensional space-fractional convection–diffusion equation using the finite volume element method to discretize the space-fractional derivative and Crank–Nicholson scheme for time discretization. We also analyze and prove the stability and convergence of the given scheme. Finally, we validate our theoretical analysis by data from three examples.
topic Fractional derivative
Finite volume element method
Stability
Convergence
Convection–diffusion equation
url https://doi.org/10.1186/s13662-021-03524-4
work_keys_str_mv AT yananbi thefinitevolumeelementmethodforthetwodimensionalspacefractionalconvectiondiffusionequation
AT ziwenjiang thefinitevolumeelementmethodforthetwodimensionalspacefractionalconvectiondiffusionequation
AT yananbi finitevolumeelementmethodforthetwodimensionalspacefractionalconvectiondiffusionequation
AT ziwenjiang finitevolumeelementmethodforthetwodimensionalspacefractionalconvectiondiffusionequation
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