TY - JOUR
T1 - Analysis of Two-Grid Methods for Nonlinear Parabolic Equations by Expanded Mixed Finite Element Methods
AU - Chen , Yanping
AU - Luan , Peng
AU - Lu , Zuliang
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 830
EP - 844
PY - 2009
DA - 2009/01
SN - 1
DO - http://doi.org/10.4208/aamm.09-m09S09
UR - https://global-sci.org/intro/article_detail/aamm/8400.html
KW - Nonlinear parabolic equations, two-grid scheme, expanded mixed finite element
methods, Gronwall's Lemma.
AB - <p style="text-align: justify;">In this paper, we present an efficient method of two-grid scheme for 
the approximation of two-dimensional nonlinear parabolic equations
using an expanded mixed finite element method. We use two Newton
iterations on the fine grid in our methods. Firstly, we solve an
original nonlinear problem on the coarse nonlinear grid, then we use
Newton iterations on the fine grid twice. The two-grid idea is from
Xu$&#39;$s work [SIAM J. Numer. Anal., 33 (1996), pp. 1759-1777] on
standard finite method. We also obtain the error estimates for the
algorithms of the two-grid method. It is shown that the algorithm
achieves asymptotically optimal approximation rate with the two-grid
methods as long as the mesh sizes satisfy
$h=\mathcal{O}(H^{(4k+1)/(k+1)})$.</p>