TY - JOUR
T1 - A Comparative Study of Finite Element and Finite Difference Methods for Two-Dimensional Space-Fractional Advection-Dispersion Equation
AU - Pang , Guofei
AU - Chen , Wen
AU - Sze , Kam Yim
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 166
EP - 186
PY - 2018
DA - 2018/05
SN - 8
DO - http://doi.org/10.4208/aamm.2014.m693
UR - https://global-sci.org/intro/article_detail/aamm/12083.html
KW - 
AB - <p style="text-align: justify;">The paper makes a comparative study of the finite element method (FEM)
and the finite difference method (FDM) for two-dimensional fractional advection-dispersion
equation (FADE) which has recently been considered a promising tool in
modeling non-Fickian solute transport in groundwater. Due to the non-local property
of integro-differential operator of the space-fractional derivative, numerical solution of
FADE is very challenging and little has been reported in literature, especially for high-dimensional
case. In order to effectively apply the FEM and the FDM to the FADE
on a rectangular domain, a backward-distance algorithm is presented to extend the
triangular elements to generic polygon elements in the finite element analysis, and a
variable-step vector Grünwald formula is proposed to improve the solution accuracy of the conventional finite difference scheme. Numerical investigation shows that the
FEM compares favorably with the FDM in terms of accuracy and convergence rate
whereas the latter enjoys less computational effort.</p>