%0 Journal Article %1 nochetto2003pointwise %A Nochetto, Ricardo H. %A Siebert, Kunibert G. %A Veeser, Andreas %D 2003 %J Numerische Mathematik %K from:mhartmann ians imported vorlaeufig %N 1 %P 163-195 %R 10.1007/s00211-002-0411-3 %T Pointwise A Posteriori Error Control for Elliptic Obstacle Problems %U http://dx.doi.org/10.1007/s00211-002-0411-3 %V 95 %X 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�lder 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.

@article{nochetto2003pointwise, 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�lder 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.}, added-at = {2018-07-20T10:54:36.000+0200}, author = {Nochetto, Ricardo H. and Siebert, Kunibert G. and Veeser, Andreas}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/219a0f381265de00f2cb2b793d95fadd4/mathematik}, doi = {10.1007/s00211-002-0411-3}, interhash = {485fe501cb1496c4cbf0e564799a304f}, intrahash = {19a0f381265de00f2cb2b793d95fadd4}, journal = {Numerische Mathematik}, keywords = {from:mhartmann ians imported vorlaeufig}, language = {English}, number = 1, owner = {kohlsk}, pages = {163-195}, timestamp = {2019-12-18T14:37:55.000+0100}, title = {Pointwise A Posteriori Error Control for Elliptic Obstacle Problems}, url = {http://dx.doi.org/10.1007/s00211-002-0411-3}, volume = 95, year = 2003 }