TY - JOUR
T1 - A Characteristic Mixed Finite Element Two-Grid Method for Compressible Miscible Displacement Problem
AU - Hu , Hanzhang
AU - Chen , Yanping
JO - Journal of Computational Mathematics
VL - 5
SP - 794
EP - 813
PY - 2022
DA - 2022/05
SN - 40
DO - http://doi.org/10.4208/jcm.2101-m2020-0277
UR - https://global-sci.org/intro/article_detail/jcm/20548.html
KW - Two-grid method, Miscible displacement problem, Mixed finite element, Characteristic finite element method.
AB - <p style="text-align: justify;">A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium. The concentration equation is treated by a mixed finite element method with characteristics (CMFEM) and the pressure equation is treated by a parabolic mixed finite element method (PMFEM). Two-grid algorithm is considered to linearize nonlinear coupled system of two parabolic partial differential equations. Moreover, the $L^q$ error estimates are conducted for the pressure, Darcy velocity and concentration variables in the two-grid solutions. Both theoretical analysis and numerical experiments are presented to show that the two-grid algorithm is very effective.</p>