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

Vincent Darrigrand, Ángel Rodríguez-Rozas, David Pardo, IGNACIO PATRICIO PEDRO MUGA URQUIZA

Research output: Contribution to journalConference articlepeer-review

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.

Original languageEnglish
Pages (from-to)848-856
Number of pages9
JournalProcedia Computer Science
Volume108
DOIs
StatePublished - 1 Jan 2017
EventInternational Conference on Computational Science ICCS 2017 - Zurich, Switzerland
Duration: 12 Jun 201714 Jun 2017

Keywords

  • Convection-Diffusion Equation
  • Error Representation
  • Finite Element Method
  • Goal-Oriented Adaptivity

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