Goal-Oriented p -Adaptivity using Unconventional Error Representations for a 1D Steady State Convection-Diffusion Problem

Abstract : This work proposes the use of an alternative error representation for Goal-Oriented Adaptivity (GOA) in context of steady state convection dominated diffusion problems. It introduces an arbitrary operator for the computation of the error of an alternative dual problem. From the new representation, we derive element-wise estimators to drive the adaptive algorithm. The method is applied to a one dimensional (1D) steady state convection dominated diffusion problem with homogeneous Dirichlet boundary conditions. This problem exhibits a boundary layer that produces a loss of numerical stability. The new error representation delivers sharper error bounds. When applied to a p-GOA Finite Element Method (FEM), the alternative error representation captures earlier the boundary layer, despite the existing spurious numerical oscillations.
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Procedia Computer Science, Elsevier, 2017, 108, pp.848-856. 〈10.1016/j.procs.2017.05.168〉
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https://hal.archives-ouvertes.fr/hal-01691499
Contributeur : Florian Faucher <>
Soumis le : mercredi 24 janvier 2018 - 09:04:59
Dernière modification le : jeudi 25 janvier 2018 - 10:19:29

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Vincent Darrigrand, Ángel Rodríguez-Rozas, David Pardo, Ignacio Muga. Goal-Oriented p -Adaptivity using Unconventional Error Representations for a 1D Steady State Convection-Diffusion Problem. Procedia Computer Science, Elsevier, 2017, 108, pp.848-856. 〈10.1016/j.procs.2017.05.168〉. 〈hal-01691499〉

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