Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method

By José Manuel Cascón, Christian Kreuzer, Ricardo H. Nochetto, Kunibert G. Siebert. SIAM Journal on Numerical Analysis, 2008

552 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6ba8e8b7931b91d5d8c0a03214a8e752b81a73c1

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

1. Andreas Veeser
2. Ricardo H. Nochetto
3. Dietmar Gallistl
4. José Manuel Cascón
5. Kunibert G. Siebert
6. G. Em Karniadakis
7. Xiaozhe Hu
8. Xuan Zhao

In Electrical and Electronic Engineering

1. Andreas Veeser
2. Dietmar Gallistl
3. Ricardo H. Nochetto
4. G. Em Karniadakis
5. Xiaozhe Hu
6. Wei Cai
7. Xuan Zhao
8. José Manuel Cascón

In Mechanics of Materials

1. Andreas Veeser
2. Ricardo H. Nochetto
3. Dietmar Gallistl
4. Kunibert G. Siebert
5. José Manuel Cascón
6. G. Em Karniadakis
7. Xiaozhe Hu
8. Wei Cai

Citations in the corpus

• Quasioptimal cardinality of AFEM driven by nonresidual estimators (2012, background): “The following two key issues, crucial in Cascón et al. (2008), must be overcome: • The estimatorη j is not reliable, namely it does not bound the energy error from above, and does not dominate the oscillation oscj .”
• Adaptive stochastic Galerkin FEM (2014, unknown): “We refer to [8] and the references therein for details.”
• 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.”
• Adaptive finite element method for fractional differential equations using hierarchical matrices (2016, methodology): “Such a posteriori error estimators have been widely discussed in the AFEM literature for second order elliptic PDEs discretized by FEM [6, 24].”
• Primer of Adaptive Finite Element Methods (2011, background): “[14].”
• Theory of adaptive finite element methods: An introduction (2009, methodology): “[21], who proved a contraction property for the quasi-error: |||u−Uk|||(2)Ω + γE 2 k (Uk,Tk), where γ > 0 is a suitable scaling constant.”