Data di Pubblicazione:
2009
Citazione:
Explicit upper bounds for dual norms of residuals / A. Veeser, R. Verfürth. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 47:3(2009), pp. 2387-2405. [10.1137/080738283]
Abstract:
We derive upper bounds for the dual norms of residuals that are explicit in terms of local Poincaré constants. Residuals are continuous linear functionals that are orthogonal to a finite element space and have a singular part supported on the skeleton of the underlying mesh. Functionals of this type play a key role in a posteriori error estimation. Our main tools are a discrete partition of unity and suitably weighted trace and Poincare' inequalities. The technique is illustrated for negative first order Sobolev norms and a dual norm arising in convection-reaction-diffusion problems.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Residual a posteriori error estimates ; guaranteed upper bounds ; dual norms ; partition of unity ; trace inequalities ; Poincaré inequalities ; robustness for singularly perturbed problems
Elenco autori:
A. Veeser, R. Verfürth
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