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A Boundary Layer Basis Method for Fractional Diffusion Equations
by
John Paul Roop
North Carolina A & T State University
In this talk, we present preliminary analytical and numerical results concerning the finite element approximation of a singularly perturbed fractional advection-dispersion equation (FADE) in one spatial dimension. The FADE is a generalization of the usual advection-dispersion equation in which the underlying stochastic process governing particle jumps is allowed to have infinite variance. We present an error estimate which indicates the under-resolved nature of the singularly perturbed FADE, as well as numerical results from a method in which the usual finite element basis is augmented by a function representing the boundary layer.
Date received: September 19, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavc-28.