Journal
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
Volume 23, Issue 2, Pages 256-281Publisher
JOHN WILEY & SONS INC
DOI: 10.1002/num.20169
Keywords
finite element method; fractional differential operator; fractional diffusion equation; fractional advection dispersion equation
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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.
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