Variational formulation for the stationary fractional advection dispersion equation. (English) Zbl 1095.65118

Ervin, Vincent J.; Roop, John Paul

Numer. Methods Partial Differ. Equations 22, No. 3, 558-576 (2006).

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 \(0\leq\beta<1\), and \(0\leq p\), \(q\leq 1\), satisfying \(p+q=1\). Convergence results are derived. Numerical calculations for piecewise linear polynomials are presented.

Reviewer: Pavol Chocholatý (Bratislava)

MSC:

65R20	Numerical methods for integral equations
26A33	Fractional derivatives and integrals
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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