Numerically solving an equation for fractional powers of elliptic operators

JOURNAL OF COMPUTATIONAL PHYSICS

卷:282

Article

Vabishchevich, Petr N.^1,2 

[1] Russian Acad Sci, Nucl Safety Inst, Moscow, Russia

[2] North Eastern Fed Univ, Yakutsk 677000, Russia

关键词: Elliptic operator;    Fractional power of an operator;    Two-level scheme;    Stability of fully discrete schemes;    Finite element approximations;   

DOI  :  10.1016/j.jcp.2014.11.022

来源: Elsevier

【 摘 要 】

An equation for a fractional power of the second-order elliptic operator is considered. It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard two-level schemes are applied. Stability conditions are obtained for the fully discrete schemes under the consideration. The numerical results are presented for a model of two-dimensional problem with a fractional power of an elliptic operator. The dependence of accuracy on grids in time and in space is studied. (C) 2014 Elsevier Inc. Allrights reserved.

【 授权许可】

Free