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Guaranteed energy error bounds for the Poisson equation using a flux‐free approach: Solving the local problems in subdomains |
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| Authors: | N. Parés H. Santos P. Díez |
| Affiliation: | 1. Escola Universitària d'Enginyeria Tècnica Industrial de Barcelona, Universitat Politècnica de Catalunya, Barcelona, Spain;2. Laboratori de Càlcul Numèric (LaCàN), Departament de Matemàtica Aplicada III, C/Jordi Girona 1‐3 E‐08034, Barcelona, Spain;3. Departamento de Engenharia Civil, Instituto Superior Técnico, Av. Rovisco Pais, 1049‐001 Lisboa, Portugal;4. Escola Tècnica Superior d'Enginyers de Camins, Canals i Ports, Universitat Politècnica de Catalunya, Barcelona, Spain;5. http://www‐lacan.upc.edu. |
| Abstract: | A method to compute guaranteed upper bounds for the energy norm of the exact error in the finite element solution of the Poisson equation is presented. The bounds are guaranteed for any finite element mesh however coarse it may be, not just in the asymptotic regime. The bounds are constructed by employing a subdomain‐based a posteriori error estimate which yields self‐equilibrated residual loads in stars (patches of elements). The proposed approach is an alternative to standard equilibrated residual methods providing sharper bounds. The use of a flux‐free error estimator improves the effectivities of the upper bounds for the energy while retaining the certainty of the bounds. Copyright © 2009 John Wiley & Sons, Ltd. |
| Keywords: | exact/guaranteed/strict bounds Poisson equation error estimation adaptivity flux‐free estimate subdomain a posteriori error estimation partition of unity residual‐based estimators |