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Zbl 1092.65122
Roop, John Paul
Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in $\mathbb R^2$. (English)
[J] J. Comput. Appl. Math. 193, No. 1, 243-268 (2006). ISSN 0377-0427

Summary: We investigate the numerical approximation of the variational solution to the fractional advection dispersion equation (FADE) on bounded domains in $\mathbb R^2$. More specifically, we investigate the computational aspects of the Galerkin approximation using continuous piecewise polynomial basis functions on a regular triangulation of the domain. The computational challenges of approximating the solution to fractional differential equations using the finite element method stem from the fact that a fractional differential operator is a nonlocal operator. Several numerical examples are given which demonstrate approximations to FADEs.

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

Keywords: finite element methods; fractional differential operators; fractional diffusion equations; fractional advection dispersion equations; Galerkin approximation; numerical examples

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