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 - <p style="text-align: justify;">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>