Exact bounds for linear outputs of the advection-diffusion-reaction equation using flux-free error estimates

Author (s): Parés, N., Díez, P., Huerta, A.
Journal: Journal on Scientific Computing (SIAM)

Volume: 31, Issue 4
Pages: 3064 – 3089
Date: 2009

Abstract:
ABSTRACT: The paper introduces a methodology to compute strict upper and lower bounds for linear-functional
outputs of the exact solutions of the advection-reaction-diffusion equation. The proposed approach is an alternative
to the standard residual type estimators (hybrid-flux), circumventing the need of flux-equilibration following a fluxfree
error estimation strategy. The presented estimator provides sharper estimates than the ones provided by both the
standard hybrid-flux techniques and other flux-free techniques.

KEYWORDS: Linear-functional outputs; Exact/guaranteed/strict bounds; Error estimation; Goal-oriented adaptivity;
Advection-reaction-diffusion equation.

Journal paper (from the publisher)  
UPCommons page Link  

Bibtex:

@article{NPM-PDH:09,
  Author   = {Par{{\'e}}s, N{{\'u}}ria and D{\'{\i}}ez, Pedro and Huerta, Antonio},
  Title    = {Exact bounds for linear outputs of the advection-diffusion-reaction equation using flux-free error estimates},
  Fjournal = {SIAM Journal on Scientific Computing},
  Journal  = {1064-8275},
  Volume   = {31},
  Number   = {4},
  Pages    = {3064--3089},
  Year     = {2009},
  Doi      = {10.1137/080724356},
  Url      = {http://www.ams.org/mathscinet-getitem?mr=2529780}}