We consider a finite element method for the elliptic obstacle problem over polyhedral domains in $\R^d$, which enforces the unilateral constraint solely at the nodes. We derive novel optimal upper and lower a posteriori error bounds in the maximum norm irrespective of mesh fineness and the regularity of the obstacle, which is just assumed to be H\"older continuous. They exhibit optimal order and localization to the non-contact set. We illustrate these results with simulations in 2d and 3d showing the impact of localization in mesh grading within the contact set along with quasi-optimal meshes.

Pointwise a posteriori error control for elliptic obstacle problems / R. H. Nochetto, K. G. Siebert, A. Veeser. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - 95:1(2003), pp. 163-195.

Pointwise a posteriori error control for elliptic obstacle problems

A. Veeser
Ultimo
2003

Abstract

We consider a finite element method for the elliptic obstacle problem over polyhedral domains in $\R^d$, which enforces the unilateral constraint solely at the nodes. We derive novel optimal upper and lower a posteriori error bounds in the maximum norm irrespective of mesh fineness and the regularity of the obstacle, which is just assumed to be H\"older continuous. They exhibit optimal order and localization to the non-contact set. We illustrate these results with simulations in 2d and 3d showing the impact of localization in mesh grading within the contact set along with quasi-optimal meshes.
elliptic obstacle problem, a posteriori error estimate, residual, maximum norm, maximum principle, barrier functions
Settore MAT/08 - Analisi Numerica
2003
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/8280
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