Abstract2018-05-24T12:52:58+00:00

Computable exact bounds for linear outputs from stabilized solutions of the advection-diffusion-reaction equation

Author (s): Parés, N.; Díez, P. and Huerta, A.
Journal: International Journal for Numerical Methods in Engineering

Volume: 93, Num. 5
Pages: 483 – 509
Date: 2013

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 bounds are computed using implicit a-posteriori error estimators from stabilized finite element approximations of the exact solution. A new methodology is introduced, based in the ideas presented in [1] for the Galerkin formulation, that allows obtaining bounds also for stabilized formulations. This methodology is combined with both hybrid-flux and flux-free techniques for error assessment. The application to stabilized formulations provides sharper estimates than when applied to Galerkin methods. The best results are found in combination with the fluxfree technique.

  
  

Bibtex:

@article{Pares-PDH:13,
  Author   = {Par{{\'e}}s, N{{\'u}}ria and D{\'{\i}}ez, Pedro and Huerta, Antonio},
  Title    = {Computable exact bounds for linear outputs from stabilized solutions of the advection-diffusion-reaction equation},
  Fjournal = {International Journal for Numerical Methods in Engineering},
  Journal  = {Int. J. Numer. Methods Eng.},
  Volume   = {93},
  Number   = {5},
  Pages    = {483--509},
  Year     = {2013},
  Doi      = {10.1002/nme.4396},
  Url      = {http://dx.doi.org/10.1002/nme.4396}}