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Zbl 1095.65118
Ervin, Vincent J.; Roop, John Paul
Variational formulation for the stationary fractional advection dispersion equation. (English)
[J] Numer. Methods Partial Differ. Equations 22, No. 3, 558-576 (2006). ISSN 0749-159X; ISSN 1098-2426/e

This paper deals with the Galerkin approximation to the steady state fractional advection dispersion equation: $-Da(p_0D_x^{-\beta}+q_x D_1^{-\beta})Du+b(x)Du+c (x)u=f$, where $D$ represents a single spatial derivative, and $_0D_x^{-\beta}$, $_xD_1^{-\beta}$ represent left and right fractional integral operators, with $0\le\beta<1$, and $0\le p$, $q\le 1$, satisfying $p+q=1$. Convergence results are derived. Numerical calculations for piecewise linear polynomials are presented.
[Pavol Chocholatý (Bratislava)]

MSC 2000:: *65R20 Integral equations (numerical methods)
26A33 Fractional derivatives and integrals (real functions)
45K05 Integro-partial differential equations

Keywords: Finite element method; fractional differential operator; fractional diffusion equation; fractional advection dispersion equation; numerical examples; Galerkin method; convergence

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Zentralblatt MATH Berlin [Germany]