Numerical solving unsteady space-fractional problems with the square root of an elliptic operator
Abstract
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed. To construct approximation in time, regularized two-level schemes are used. The numerical implementation is based on solving the equation with the square root of the elliptic operator using an auxiliary Cauchy problem for a pseudo-parabolic equation. The scheme of the second-order accuracy in time is based on a regularization of the three-level explicit Adams scheme. More general problems for the equation with convective terms are considered, too. The results of numerical experiments are presented for a model two-dimensional problem.
Keywords
Cite
@article{arxiv.1510.08297,
title = {Numerical solving unsteady space-fractional problems with the square root of an elliptic operator},
author = {Petr N. Vabishchevich},
journal= {arXiv preprint arXiv:1510.08297},
year = {2015}
}
Comments
21 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1412.5706