Why Adaptive Finite Element Methods Outperform Classical Ones

Ricardo H. Nochetto
2011 Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)  
Adaptive finite element methods (AFEM) are a fundamental numerical tool in science and engineering. They are known to outperform classical FEM in practice and deliver optimal convergence rates when the latter cannot. This paper surveys recent progress in the theory of AFEM which explains their success and provides a solid mathematical framework for further developments. Mathematics Subject Classification (2010). Primary 65N30, 65N50, 65N15; Secondary 41A25.
doi:10.1142/9789814324359_0168 fatcat:5l4jr6q7cjaglffkeylanwhl6m