Numerical Solution of Nonstationary Problems for a Convection and a Space-Fractional Diffusion Equation

Numerical Solution of Nonstationary Problems for a Convection and a Space-Fractional Diffusion Equation

Year:    2016

International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 2 : pp. 296–309

Abstract

Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. An unsteady problem is considered for a convection and a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary conditions of Robin type. 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 fractional power of the elliptic operator using an auxiliary Cauchy problem for a pseudo-parabolic equation. The results of numerical experiments are presented for a model two-dimensional problem.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2016-IJNAM-440

International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 2 : pp. 296–309

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Convection-diffusion problem fractional partial differential equations elliptic operator fractional power of an operator two-level difference scheme.