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Volume 8, Issue 3
A Two-Grid Finite Element Method for Nonlinear Sobolev Equations

Chuanjun Chen & Kang Li

East Asian J. Appl. Math., 8 (2018), pp. 549-565.

Published online: 2018-08

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  • 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.

  • AMS Subject Headings

65N12, 65M60

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-549, author = {Chuanjun Chen and Kang Li}, title = {A Two-Grid Finite Element Method for Nonlinear Sobolev Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.150117.260618}, url = {http://global-sci.org/intro/article_detail/eajam/12625.html} }
TY - JOUR T1 - A Two-Grid Finite Element Method for Nonlinear Sobolev Equations AU - Chuanjun Chen & Kang Li JO - East Asian Journal on Applied Mathematics VL - 3 SP - 549 EP - 565 PY - 2018 DA - 2018/08 SN - 8 DO - http://doi.org/10.4208/eajam.150117.260618 UR - https://global-sci.org/intro/article_detail/eajam/12625.html KW - Nonlinear Sobolev equations, two-grid finite element method, error estimate. AB -

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.

Chuanjun Chen and Kang Li. (2018). A Two-Grid Finite Element Method for Nonlinear Sobolev Equations. East Asian Journal on Applied Mathematics. 8 (3). 549-565. doi:10.4208/eajam.150117.260618
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