Pointwise a posteriori error control for elliptic obstacle problems. (English) Zbl 1027.65089

Nochetto, Ricardo H.; Siebert, Kunibert G.; Veeser, Andreas

Numer. Math. 95, No. 1, 163-195 (2003).

The authors develop a finite element method for the elliptic obstacle problem over polyhedral domains in \(\mathbb{R}^d\), which enforces the unilateral constraint solely at the nodes. Optimal upper and lower a posteriori error bounds are derived in the maximum norm irrespective of mesh finesse and the regularity of the obstacle (just assumed to be Hölder continuous). Simulation in 2D and 3D are given for showing the impact of localization in mesh grading within the contact set along with quasi-optimal meshes.

Reviewer: Yves Cherruault (Paris)

MSC:

65K10	Numerical optimization and variational techniques
49J20	Existence theories for optimal control problems involving partial differential equations
49M15	Newton-type methods

Keywords:

elliptic obstacle problem; a posteriori error bounds; finite element method

Software:

ALBERT