TY - JOUR
T1 - A Two-Grid Finite Element Method for Nonlinear Sobolev Equations
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 - <p style="text-align: justify;">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.</p>