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.
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]
Explicit upper bounds for dual norms of residuals
A. VeeserPrimo
;
2009
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.Pubblicazioni consigliate
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