Variational formulation for the stationary fractional advection dispersion equation

被引：646

作者：

Ervin, VJ ^{[1
]}

Roop, JP ^{[1
]}

机构：

[1] Clemson Univ, Dept Math Sci, Clemson, SC 29634 USA

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2006年 / 22卷 / 03期

关键词：

finite element method; fractional differential operator; fractional diffusion equation; fractional advection dispersion equation;

D O I：

10.1002/num.20112

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 H-s. Existence and uniqueness results are proven, and error estimates for the Galerkin approximation derived. Numerical results are included that confirm the theoretical estimates. (C) 2005 Wiley Periodicals, Inc.

引用

页码：558 / 576

页数：19

共 14 条

[1]

[Anonymous], 1975, SOBOLOV SPACES

[2] The fractional-order governing equation of Levy motion [J].