TY - JOUR
T1 - Two-Grid Finite Element Methods of Crank-Nicolson Galerkin Approximation for a Nonlinear Parabolic Equation
AU - Tan , Zhijun
AU - Li , Kang
AU - Chen , Yanping
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 800
EP - 817
PY - 2020
DA - 2020/08
SN - 10
DO - http://doi.org/10.4208/eajam.030120.120520
UR - https://global-sci.org/intro/article_detail/eajam/17962.html
KW - Nonlinear parabolic equation, finite element method, two-grid, Crank-Nicolson Galerkin scheme, optimal convergence order.
AB - <p style="text-align: justify;">Two-grid finite element methods with the Crank-Nicolson Galerkin scheme
for nonlinear parabolic equations are studied. It is shown that the methods have convergence order $\mathcal{O}$($h$ + $H$<sup>2</sup> + (∆$t$)<sup>2</sup>) in $H$<sup>1</sup>-norm, so that a larger time step can be used
in numerical calculations. In addition to saving computing time, the algorithms provide
a good approximation of the problem solution and numerical examples confirm their
efficiency.</p>