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Two-Grid Finite Element Methods of Crank-Nicolson Galerkin Approximation for a Nonlinear Parabolic Equation

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.

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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

Zhijun Tan

Kang Li

Yanping Chen

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