Year: 2015
International Journal of Numerical Analysis and Modeling, Vol. 12 (2015), Iss. 2 : pp. 197–210
Abstract
A two-grid algorithm is presented and discussed for a finite volume element method to a nonlinear parabolic equation in a convex polygonal domain. The two-grid algorithm consists of solving a small nonlinear system on a coarse-grid space with grid size $H$ and then solving a resulting linear system on a fine-grid space with grid size $h$. Error estimates are derived with the $H^1$-norm $O(h+H^2)$ which shows that the two-grid algorithm achieves asymptotically optimal approximation as long as the mesh sizes satisfy $h=O(H^2)$. Numerical examples are presented to validate the usefulness and efficiency of the method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2015-IJNAM-484
International Journal of Numerical Analysis and Modeling, Vol. 12 (2015), Iss. 2 : pp. 197–210
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Two-grid finite volume element method nonlinear parabolic equation error estimates.