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

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...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2008-03, Vol.197 (19), p.1661-1679
Main Authors: Parés, Núria, Díez, Pedro, Huerta, Antonio
Format: Article
Language:English
Subjects:
Anàlisi numèrica
Computational techniques
Error bounds
Error estimation
Exact sciences and technology
Exact/guaranteed/strict bounds
Fundamental areas of phenomenology (including applications)
Goal-oriented adaptivity
Linear-functional outputs
Matemàtiques i estadística
Mathematical methods in physics
Numerical analysis
Parabolic problems
Physics
Space–time adaptivity
Àrees temàtiques de la UPC
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Summary: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.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2007.08.024