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.

EUDML-ID : urn:eudml:doc:287835
Mots clés:
Mots clés:

@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/