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2012 A Two-Grid Method for Finite Element Solutions of Nonlinear Parabolic Equations
Chuanjun Chen, Wei Liu
Abstr. Appl. Anal. 2012(SI06): 1-11 (2012). DOI: 10.1155/2012/391918


A two-grid method is presented and discussed for a finite element approximation to a nonlinear parabolic equation in two space dimensions. Piecewise linear trial functions are used. In this two-grid scheme, the full nonlinear problem is solved only on a coarse grid with grid size H . The nonlinearities are expanded about the coarse grid solution on a fine gird of size h , and the resulting linear system is solved on the fine grid. A priori error estimates are derived with the H 1 -norm O ( h + H 2 ) which shows that the two-grid method achieves asymptotically optimal approximation as long as the mesh sizes satisfy h = O ( H 2 ) . An example is also given to illustrate the theoretical results.


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Chuanjun Chen. Wei Liu. "A Two-Grid Method for Finite Element Solutions of Nonlinear Parabolic Equations." Abstr. Appl. Anal. 2012 (SI06) 1 - 11, 2012.


Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1253.65159
MathSciNet: MR2975310
Digital Object Identifier: 10.1155/2012/391918

Rights: Copyright © 2012 Hindawi


Vol.2012 • No. SI06 • 2012
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