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Variational formulation for the stationary fractional advection dispersion equation
Author(s) -
Ervin Vincent J.,
Roop John Paul
Publication year - 2006
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.20112
Subject(s) - mathematics , fractional calculus , sobolev space , uniqueness , galerkin method , mathematical analysis , partial differential equation , partial derivative , advection , dimension (graph theory) , derivative (finance) , finite element method , pure mathematics , physics , thermodynamics , financial economics , economics
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. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005