Bounds of functional outputs for parabolic problems. Part II: Bounds of the exact solution

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

Volume: 197, Issues 19-20
Pages: 1661 – 1679
Date: 2008

Abstract:
The paper introduces a methodology to compute upper and lower bounds for linear-functional
outputs of the exact solutions of parabolic problems. In this second part, the bounds account
for the error both in space and time. The assumption stating that the error introduced by the
time marching scheme is negligible, used in the first part, is removed here. The bounds are
computed starting from an approximation of the exact solution, associated with a spatial
mesh and a time grid. Nevertheless, the bounds are guaranteed with respect to the exact
solution, with no reference to any mesh or time discretization.

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Bibtex:

@article{NPM-PDH:08b,
  Author   = {Par{{\'e}}s, N{{\'u}}ria and D{\'{\i}}ez, Pedro and Huerta, Antonio},
  Title    = {Bounds of functional outputs for parabolic problems. {II}. {B}ounds of the exact solution},
  Fjournal = {Computer Methods in Applied Mechanics and Engineering},
  Journal  = {Comput. Methods Appl. Mech. Eng.},
  Volume   = {197},
  Number   = {19-20},
  Pages    = {1661--1679},
  Year     = {2008},
  Doi      = {10.1016/j.cma.2007.08.024},
  Url      = {http://dx.doi.org/10.1016/j.cma.2007.08.024}}