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Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in \(\mathbb R^2\). (English) Zbl 1092.65122
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.

65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
26A33 Fractional derivatives and integrals
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