East Asian J. Appl. Math., 8 (2018), pp. 549-565.
Published online: 2018-08
Cited by
- BibTex
- RIS
- TXT
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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.150117.260618}, url = {http://global-sci.org/intro/article_detail/eajam/12625.html} }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.