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

https://doi.org/10.1016/j.procs.2017.05.168Get rights and content
Under a Creative Commons license
open access

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.

Keywords

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

Cited by (0)