A new equilibrated residual method improving accuracy and efficiency of flux-free error estimates

Author (s): N. Parés, N. and Díez, P.
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 313, Issue 1
Pages: 785 – 816
Date: 2017

Abstract:
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 [20, 18] with the goal of substantially reducing the com- putational 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 up- per bounds for the energy and requires only doubling the dimension of the local linear systems of equations to be solved.

Journal paper (from the publisher)  
UPCommons page Link  

Bibtex:

@article{Parés2017785,
author = "Parés, N. and Díez, P.“,
title = "A new equilibrated residual method improving accuracy and efficiency of flux-free error estimates ",
journal = "Computer Methods in Applied Mechanics and Engineering ",
volume = "313",
number = “1”,
pages = "785 - 816",
year = "2017",
issn = "0045-7825",
doi = "http://dx.doi.org/10.1016/j.cma.2016.10.010",
url = "http://www.sciencedirect.com/science/article/pii/S004578251630250X",
keywords = “Exact/guaranteed/strict bounds; Fully computable a posteriori error estimation; Adaptivity; Reaction–diffusion equation; Flux-free; Equilibrated boundary tractions”
}