A BASIC CONVERGENCE RESULT FOR CONFORMING ADAPTIVE FINITE ELEMENTS
By Pedro Morin, Kunibert G. Siebert, Andreas Veeser. 2008
192 citations recorded by the source corpus.
We consider the approximate solution with adaptive finite elements of a class of linear boundary value problems, which includes problems of "saddle point" type. For the adaptive algorithm we assume the following framework: refinement relies on unique quasi-regular element subdivisions and generates locally quasi-uniform grids, the finite element spaces are conforming, nested, and satisfy the inf–sup conditions, the error estimator is reliable as well as locally and discretely efficient, and marked elements are subdivided at least once. Under these assumptions, we give a sufficient and essentially necessary condition on marking for the convergence of the finite element solutions to the exact one. This condition is not only satisfied by Dorfler's strategy, but also by the maximum strategy and the equidistribution strategy.
View Paper: https://www.semanticscholar.org/paper/13a833ad5e590dbad4adb591230f95e4c4420cbb
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Ricardo H. Nochetto
- Andreas Veeser
- Juan P. Agnelli
- E. M. Garau
- Pedro Morin
- Hengguang Li
- Rob P. Stevenson
- Kunibert G. Siebert
Citations in the corpus
- Quasioptimal cardinality of AFEM driven by nonresidual estimators (2012, background): “Hierarchical estimators have been proposed by Bornemannet al. (1996) and further developed in Veeser (2002); Verfürth (1996).”
- Theory of adaptive finite element methods: An introduction (2009, unknown): “[55] and the modifications by Siebert [67].”
- Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method (2008, unknown): “The first convergence result for such a standard AFEM is due to Morin, Siebert, and Veeser [19].”
- Primer of Adaptive Finite Element Methods (2011, methodology): “Examples are the convergence analyses for the p-Laplacian by Veeser [55] and for the obstacle problem by Siebert and Veeser [51], which are the first steps in the terrain of nonlinear and nonsmooth problems and are predecessors of [44, 49].”
- A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces (2014, background): “3), allowing us to conclude convergence of adaptive methods by resorting to the general theory developed in [22, 29].”