A new equilibrated residual method improving accuracy and efficiency of flux-free error estimates
This paper presents a new methodology to compute guaranteed upper bounds for the energy norm of the error in the context of linear finite element approximations of the reaction–diffusion equation. The new approach revisits the ideas in Parés et al. (2009) [6, 4], with the goal of substantially reduc...
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| Veröffentlicht in: | Computer methods in applied mechanics and engineering 2017-01, Vol.313, p.785-816 |
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| container_title | Computer methods in applied mechanics and engineering |
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| creator | Parés, N. Díez, P. |
| description | This paper presents a new methodology to compute guaranteed upper bounds for the energy norm of the error in the context of linear finite element approximations of the reaction–diffusion equation. The new approach revisits the ideas in Parés et al. (2009) [6, 4], with the goal of substantially reducing the computational cost of the flux-free method while retaining the good quality of the bounds. The new methodology provides also a technique to compute equilibrated boundary tractions improving the quality of standard equilibration strategies. The zeroth-order equilibration conditions are imposed using an alternative less restrictive form of the first-order equilibration conditions, along with a new efficient minimization criterion. This new equilibration strategy provides much more accurate upper bounds for the energy and requires only doubling the dimension of the local linear systems of equations to be solved. |
| doi_str_mv | 10.1016/j.cma.2016.10.010 |
| format | Article |
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| identifier | ISSN: 0045-7825 |
| ispartof | Computer methods in applied mechanics and engineering, 2017-01, Vol.313, p.785-816 |
| issn | 0045-7825 1879-2138 |
| language | eng |
| recordid | cdi_csuc_recercat_oai_recercat_cat_2072_272026 |
| source | Recercat; Elsevier ScienceDirect Journals |
| subjects | Accuracy Adaptivity Anàlisi numèrica Balancing Boundary layer Computational efficiency Cost engineering Equilibrated boundary tractions Exact/guaranteed/strict bounds Finite element method Flux Flux-free Fully computable a posteriori error estimation Linear systems Matemàtiques i estadística Mètodes en elements finits Numerical analysis Reaction–diffusion equation Upper bounds Àrees temàtiques de la UPC |
| title | A new equilibrated residual method improving accuracy and efficiency of flux-free error estimates |
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