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Variational solution of fractional advection dispersion equations on bounded domains in ℝ d
Author(s) -
Ervin Vincent J.,
Roop John Paul
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20169
Subject(s) - mathematics , fractional calculus , bounded function , uniqueness , sobolev space , mathematical analysis , dispersion (optics) , partial differential equation , physics , optics
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. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 256–281, 2007