Subdomain-based flux-free a posteriori error estimators

• Published in: Computer methods in applied mechanics and engineering Vol. 195; no. 4; pp. 297 - 323
• Main Authors: Parés, Núria, Díez, Pedro, Huerta, Antonio
• Format: Journal Article Conference Proceeding Publication
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2006; Elsevier
• Subjects: Anàlisi d'error (Matemàtica); Anàlisi numèrica; Computational techniques; Engineering outputs; Error analysis (Mathematics); Error bounds; Error estimation; Exact sciences and technology; Functional outputs; Fundamental areas of phenomenology (including applications); Goal-oriented error estimation; Matemàtiques i estadística; Mathematical methods in physics; Physics; Residual-based estimators; Àrees temàtiques de la UPC; Residual-based estimators; Error bounds; Error estimation; Goal-oriented error estimation; Engineering outputs; Functional outputs; Finite element method; Lower bound; Upper bound; A posteriori estimation; Modelling; Domain decomposition
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2004.06.047

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.