Paper Info
Title
Convergence of Adaptive Finite Element Methods.
Abstract
Adaptive finite element methods (FEMs) have been widely used in applications for over 20 years now. In practice, they converge starting from coarse grids, although no mathematical theory has been able to prove this assertion. Ensuring an error reduction rate based on a posteriori error estimators, together with a reduction rate of data oscillation (information missed by the underlying averaging process), we construct a simple and efficient adaptive FEM for elliptic partial differential equations. We prove that this algorithm converges with linear rate without any preliminary mesh adaptation nor explicit knowledge of constants. Any prescribed error tolerance is thus achieved in a finite number of steps. A number of numerical experiments in two and three dimensions yield quasi-optimal meshes along with a competitive performance. Extensions to higher order elements and applications to saddle point problems are discussed as well.
Year
DOI
Venue
2002
10.1137/S0036144502409093
SIAM Review
Keywords
DocType
Volume
prescribed error tolerance,reduction rate,algorithm converges,efficient adaptive fem,adaptive finite element methods,finite number,posteriori error estimator,coarse grid,error reduction rate,adaptive finite element method,linear rate,oscillations,convergence,adaptive mesh refinement
Journal
44
Issue
Citations 
PageRank 
4
60
3.23
References 
Authors
0
3
Name
Order
Citations
PageRank
Pedro Morin133147.99
Ricardo H. Nochetto2907110.08
Kunibert G. Siebert347151.43