Optimality of a Standard Adaptive Finite Element Method

By Rob P. Stevenson. Foundations of Computational Mathematics, 2007

515 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6e1eb25d9d78cac6da0b3e97d99dbc830f9c6e9b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Theory of adaptive finite element methods: An introduction (2009, methodology): “This approach allows us to include variable data f and A and thus improves upon and extends Stevenson [69].”
Primer of Adaptive Finite Element Methods (2011, methodology): “[7] and Stevenson [52] arrange the a posteriori analysis such that oscillation is measured in H .”
Morley Finite Element Method for the Eigenvalues of the Biharmonic Operator (2014, methodology): “The proofs follow the methodology of [17, 38] which has already been applied in [21, 16, 13] for simple eigenvalues, in [20] for multiple eigenvalues, and in [25, 24] for clustered eigenvalues.”
Approximation of high-dimensional parametric PDEs * (2015, background): “Let us point out that a similar objective can be attained when considering the spatial discretization of a single PDE, by either adaptive wavelet methods [21, 22, 38] or by adaptive finite element methods [70, 7, 86].”
Tractability of Multivariate Problems (2008, background): “, the papers by Cohen, Dahmen and DeVore [31], Dahlke, Dahmen and DeVore [35] and Stevenson [221].”
Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs (2011, methodology): “We should point out that a similar program was developed when solving a single PDE by either adaptive wavelet methods [7,8,14] or by adaptive finite element methods [4,12,21,26].”
The completion of locally refined simplicial partitions created by bisection (2008, background): “Citation for published version (APA): Stevenson, R. (2008). The completion of locally refined simplicial partitions created by bisection.”
A review of unified a posteriori finite element error control (2012, background): “We note that these issues have been initiated in [31] and subsequently studied in [10,42] and [26].”
Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method (2008, unknown): “This slightly improves a similar result by Stevenson [23] in the sense that the error can be estimated here by using only the indicators of refined elements without a buffer layer.”