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.
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}} 
