We review some numerical analysis of an adaptive finite element method (AFEM) for a class of elliptic partial differential equations based on a perturbation argument. This argument makes use of the relationship between the general problem and a model problem, whose adaptive finite element analysis is existing, from which we get the convergence and the complexity of adaptive finite element methods for a nonsymmetric boundary value problem, an eigenvalue problem, a nonlinear boundary value problem as well as a nonlinear eigenvalue problem.
@article{702893,
title = {Adaptive finite element analysis based on perturbation arguments},
booktitle = {Applications of Mathematics 2012},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2012},
pages = {62-71},
mrnumber = {MR3204453},
zbl = {1313.65300},
url = {http://dml.mathdoc.fr/item/702893}
}
Dai, Xiaoying; He, Lianhua; Zhou, Aihui. Adaptive finite element analysis based on perturbation arguments, dans Applications of Mathematics 2012, GDML_Books, (2012), pp. 62-71. http://gdmltest.u-ga.fr/item/702893/