Year: 2018
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 3 : pp. 549–565
Abstract
A two-grid based finite element method for nonlinear Sobolev equations is studied. It consists in solving small nonlinear systems related to coarse-grids, following the solution of linear systems in fine-grid spaces. The method has the same accuracy as the standard finite element method but reduces workload and saves CPU time. The $H^1$-error estimates show that the two-grid methods have optimal convergence if the coarse $H$ and fine $h$ mesh sizes satisfy the condition $h=\mathscr{O}(H^2)$. Numerical examples confirm the theoretical findings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.150117.260618
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 3 : pp. 549–565
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Nonlinear Sobolev equations two-grid finite element method error estimate.
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