Variational formulation for the stationary fractional advection dispersion equation

Vincent J. Ervin; John Paul Roop

doi:10.1002/num.20112

Variational formulation for the stationary fractional advection dispersion equation

Vincent J. Ervin
, John Paul Roop

Mathematics and Statistics

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

702 Scopus citations

Abstract

In this article a theoretical framework for the Galerkin finite element approximation to the steady state fractional advection dispersion equation is presented. Appropriate fractional derivative spaces are defined and shown to be equivalent to the usual fractional dimension Sobolev spaces Hs. Existence and uniqueness results are proven, and error estimates for the Galerkin approximation derived. Numerical results are included that confirm the theoretical estimates. © 2005 Wiley Periodicals, Inc.

Original language	English
Pages (from-to)	558-576
Number of pages	19
Journal	Numerical Methods for Partial Differential Equations
Volume	22
Issue number	3
DOIs	https://doi.org/10.1002/num.20112
State	Published - Jan 1 2006

Keywords

Finite element method
Fractional advection dispersion equation
Fractional differential operator
Fractional diffusion equation

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10.1002/num.20112

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AB - In this article a theoretical framework for the Galerkin finite element approximation to the steady state fractional advection dispersion equation is presented. Appropriate fractional derivative spaces are defined and shown to be equivalent to the usual fractional dimension Sobolev spaces Hs. Existence and uniqueness results are proven, and error estimates for the Galerkin approximation derived. Numerical results are included that confirm the theoretical estimates. © 2005 Wiley Periodicals, Inc.

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KW - Fractional advection dispersion equation

KW - Fractional differential operator

KW - Fractional diffusion equation

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Variational formulation for the stationary fractional advection dispersion equation

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