TY - JOUR
T1 - A Posteriori Estimator of Nonconforming Finite Element Method for Fourth Order Elliptic Perturbation Problems
JO - Journal of Computational Mathematics
VL - 4
SP - 554
EP - 577
PY - 2008
DA - 2008/08
SN - 26
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8642.html
KW - Fourth order elliptic perturbation problems, Nonconforming finite element
method, A posteriori error estimator, Adaptive algorithm, Local behavior.
AB - <p style="text-align: justify;">In this paper, we consider the nonconforming finite element approximations of fourth order elliptic perturbation problems in two dimensions. We present an $a posteriori$ error estimator under certain conditions, and give an $h$-version adaptive algorithm based on the error estimation. The local behavior of the estimator is analyzed as well. This estimator works for several nonconforming methods, such as the modified Morley method and the modified Zienkiewicz method, and under some assumptions, it is an optimal one. Numerical examples are reported, with a linear stationary Cahn-Hilliard-type equation as a model problem.</p>