TY - JOUR
T1 - Crank-Nicolson Method of a Two-Grid Finite Volume Element Algorithm for Nonlinear Parabolic Equations
AU - Gong , Yunjie
AU - Chen , Chuanjun
AU - Lou , Yuzhi
AU - Xue , Guanyu
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 540
EP - 559
PY - 2021
DA - 2021/05
SN - 11
DO - http://doi.org/10.4208/eajam.090820.311220
UR - https://global-sci.org/intro/article_detail/eajam/19140.html
KW - Crank-Nicolson method, two-grid algorithm, finite volume element method, error estimates, nonlinear parabolic equations.
AB - <p style="text-align: justify;">A two-grid finite volume element algorithm based on Crank-Nicolson scheme
for nonlinear parabolic equations is proposed. In this method, the nonlinear problem is
solved on a coarse grid of size $H$ and a linear problem is considered on a fine grid of size $h$ by using the coarse-grid solution and one Newton iteration. This helps to improve the
computing efficiency while keeping the accuracy. It is proved that the two-grid method
can achieve asymptotically optimal error estimates in spaces and second order accuracy
in time. Numerical results are consistent with the theoretical findings.</p>