Two-Grid Finite Element Methods of Crank-Nicolson Galerkin Approximation for a Nonlinear Parabolic Equation
Year: 2020
Author: Zhijun Tan, Kang Li, Yanping Chen
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 800–817
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.030120.120520
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 800–817
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Nonlinear parabolic equation finite element method two-grid Crank-Nicolson Galerkin scheme optimal convergence order.
Author Details
-
Two-grid fully discrete finite element algorithms on temporal graded meshes for nonlinear multi-term time-fractional diffusion equations with variable coefficient
Li, Kang | Tan, ZhijunCommunications in Nonlinear Science and Numerical Simulation, Vol. 125 (2023), Iss. P.107360
https://doi.org/10.1016/j.cnsns.2023.107360 [Citations: 4] -
A two-grid discretization method for nonlinear Schrödinger equation by mixed finite element methods
Tian, Zhikun | Chen, Yanping | Wang, JianyunComputers & Mathematics with Applications, Vol. 130 (2023), Iss. P.10
https://doi.org/10.1016/j.camwa.2022.11.015 [Citations: 1] -
Two-Grid Method for a Fully Discrete Mixed Finite Element Solution of the Time-Dependent Schrödinger Equation
Tian, Zhikun | Chen, Yanping | Wang, JianyunMathematics, Vol. 11 (2023), Iss. 14 P.3127
https://doi.org/10.3390/math11143127 [Citations: 1]