Subdomain-based flux-free a posteriori error estimators
By Núria Parés, Pedro Díez, Antonio Huerta. 2006
127 citations recorded by the source corpus.
A new residual type flux-free error estimator is presented. It estimates upper and lower bounds of the error in energy norm. The proposed approach precludes the main drawbacks of standard residual type estimators, circumvents the need of flux-equilibration and results in a simple implementation that uses standard resources available in finite element codes. This is specially interesting for 3D applications where the implementation of this technique is as simple as in 2D. Recall that on the contrary, the complexity of the flux-equilibration techniques increases drastically in the 3D case. The bounds for the energy norm of the error are used to produce upper and lower bounds of linear functional outputs, representing quantities of engineering interest. The presented estimators demonstrate their efficiency in numerical tests producing sharp estimates both for the energy and the quantities of interest.
Subfields: Computational Mechanics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/446e71b7aa95293e1a153181e1050b45b9cfbb44
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In Computational Mechanics
- Antonio Huerta
- S. Fernández‐Méndez
- Giorgio Giorgiani
- Régis Cottereau
- Pedro Díez
- John Dolbow
- Dominik Schillinger
- Xiaoying Zhuang
In Statistical and Nonlinear Physics
Citations in the corpus
- Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method (2009, methodology): “They differ by the type of functions and the way in which they are introduced in the equations, and we will here follow the method described in [13,19].”
- Hybridizable discontinuous Galerkin p‐adaptivity for wave propagation problems (2013, background): “But a posteriori error estimators have a non trivial computational overhead when recovery techniques are used [56], or when equilibrated fluxes must be computed [57] and also in flux-free implementations [58].”