Variational solution of fractional advection dispersion equations on bounded domains in Rd
Variational solution of fractional advection dispersion equations on bounded domains in Rd
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DOI：
10.1002/num.20169
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发表时间：
2007-03-01
影响因子：
3.9
通讯作者：
Roop, John Paul
中科院分区：
文献类型：
--
作者：
Ervin, Vincent J.;Roop, John Paul
本文讨论了R-d中有界区域上的定态分数阶对流弥散方程。定义并分析了分数阶微分算子和分数阶积分算子。定义了适当的分数导数空间，并证明了它与分数维Sobolev空间是等价的。稳态FADE的变分解的理论框架。存在性和唯一性结果的证明，并获得有限元逼近的误差估计。(c)2006 Wiley Periodicals，Inc.
In this article, we discuss the steady state fractional advection dispersion equation (FADE) on bounded domains in R-d. Fractional differential and integral operators are defined and analyzed. Appropriate fractional derivative spaces are defined and shown to be equivalent to the fractional dimensional Sobolev spaces. A theoretical framework for the variational solution of the steady state FADE is presented. Existence and uniqueness results are proven, and error estimates obtained for the finite element approximation. (c) 2006 Wiley Periodicals, Inc.