Variational solution of fractional advection dispersion equations on bounded domains in ℝ  d | Zendy

Ervin Vincent J. | Zendy; Roop John Paul | Zendy

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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

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