We introduce a stabilised finite element formulation for the Kirchhoff plate obstacle problem and derive both a priori and residual-based a posteriori error estimates using conforming \$\$C^1\$\$C1-continuous finite elements. We implement the method as a Nitsche-type scheme and give numerical evidence for its effectiveness in the case of an elastic and a rigid obstacle.
%0 Journal Article
%1 gustafsson2019stabilised
%A Gustafsson, Tom
%A Stenberg, Rolf
%A Videman, Juha
%D 2019
%J BIT Numerical Mathematics
%K 47j20-variational-and-other-inequalities-involving-nonlinear-operators 49j40-variational-inequalities 65n30-pdes-bvps-finite-elements 74k20-plates 74s05-finite-element-methods-for-solid-mechanics
%N 1
%P 97--124
%R 10.1007/s10543-018-0728-7
%T A stabilised finite element method for the plate obstacle problem
%U https://link.springer.com/article/10.1007%2Fs10543-018-0728-7
%V 59
%X We introduce a stabilised finite element formulation for the Kirchhoff plate obstacle problem and derive both a priori and residual-based a posteriori error estimates using conforming \$\$C^1\$\$C1-continuous finite elements. We implement the method as a Nitsche-type scheme and give numerical evidence for its effectiveness in the case of an elastic and a rigid obstacle.
@article{gustafsson2019stabilised,
abstract = {We introduce a stabilised finite element formulation for the Kirchhoff plate obstacle problem and derive both a priori and residual-based a posteriori error estimates using conforming {\$}{\$}C^1{\$}{\$}C1-continuous finite elements. We implement the method as a Nitsche-type scheme and give numerical evidence for its effectiveness in the case of an elastic and a rigid obstacle.},
added-at = {2020-02-19T00:20:34.000+0100},
author = {Gustafsson, Tom and Stenberg, Rolf and Videman, Juha},
biburl = {https://www.bibsonomy.org/bibtex/285e01a8f5bf453d74ef405d523a513be/gdmcbain},
day = 01,
doi = {10.1007/s10543-018-0728-7},
interhash = {7caf950681b4699f93b8835ceeec3d27},
intrahash = {85e01a8f5bf453d74ef405d523a513be},
issn = {1572-9125},
journal = {BIT Numerical Mathematics},
keywords = {47j20-variational-and-other-inequalities-involving-nonlinear-operators 49j40-variational-inequalities 65n30-pdes-bvps-finite-elements 74k20-plates 74s05-finite-element-methods-for-solid-mechanics},
month = mar,
number = 1,
pages = {97--124},
timestamp = {2020-02-19T00:49:34.000+0100},
title = {A stabilised finite element method for the plate obstacle problem},
url = {https://link.springer.com/article/10.1007%2Fs10543-018-0728-7},
volume = 59,
year = 2019
}