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Volume 10, Issue 4
Two-Grid Finite Element Methods of Crank-Nicolson Galerkin Approximation for a Nonlinear Parabolic Equation

Zhijun Tan, Kang Li & Yanping Chen

DOI: 10.4208/eajam.030120.120520

East Asian J. Appl. Math., 10 (2020), pp. 800-817.

Published online: 2020-08

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  • 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.

  • Keywords

Nonlinear parabolic equation, finite element method, two-grid, Crank-Nicolson Galerkin scheme, optimal convergence order.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-10-800, author = {Tan , ZhijunLi , Kang and Chen , Yanping}, title = {Two-Grid Finite Element Methods of Crank-Nicolson Galerkin Approximation for a Nonlinear Parabolic Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.030120.120520}, url = {http://global-sci.org/intro/article_detail/eajam/17962.html} }
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.

Tan , ZhijunLi , Kang and Chen , Yanping. (2020). Two-Grid Finite Element Methods of Crank-Nicolson Galerkin Approximation for a Nonlinear Parabolic Equation. East Asian Journal on Applied Mathematics. 10 (4). 800-817. doi:10.4208/eajam.030120.120520
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