Finite element approximations for fractional evolution problems
Numerical Analysis
2018-04-17 v2
Abstract
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we consider is employed to represent memory effects, while a nonlocal differentiation operator in space accounts for long-range dispersion processes. We discuss well-posedness and obtain regularity estimates for the evolution problems under consideration. The discrete scheme we develop is based on piecewise linear elements for the space variable and a convolution quadrature for the time component. We illustrate the method's performance with numerical experiments in one- and two-dimensional domains.
Cite
@article{arxiv.1705.09815,
title = {Finite element approximations for fractional evolution problems},
author = {Gabriel Acosta and Francisco M. Bersetche and Juan Pablo Borthagaray},
journal= {arXiv preprint arXiv:1705.09815},
year = {2018}
}