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Volume 13, Issue 2
Numerical Solution of Nonstationary Problems for a Convection and a Space-Fractional Diffusion Equation

P. Vabishchevich

Int. J. Numer. Anal. Mod., 13 (2016), pp. 296-309.

Published online: 2016-03

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  • 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.

  • Keywords

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

  • AMS Subject Headings

26A33, 35R11, 65F60, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-296, author = {P. Vabishchevich}, title = {Numerical Solution of Nonstationary Problems for a Convection and a Space-Fractional Diffusion Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/440.html} }
TY - JOUR T1 - Numerical Solution of Nonstationary Problems for a Convection and a Space-Fractional Diffusion Equation AU - P. Vabishchevich JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 296 EP - 309 PY - 2016 DA - 2016/03 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/440.html KW - Convection-diffusion problem, fractional partial differential equations, elliptic operator, fractional power of an operator, two-level difference scheme. AB -

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.

P. Vabishchevich. (2016). Numerical Solution of Nonstationary Problems for a Convection and a Space-Fractional Diffusion Equation. International Journal of Numerical Analysis and Modeling. 13 (2). 296-309. doi:
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