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 -

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$2 + (∆$t$)2) in $H$1-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.