This paper focusses on the von Kármán equations for the moderately large deformation of a very thin plate with the convex obstacle constraint leading to a coupled system of semilinear fourth-order obstacle problem and motivates its nonconforming Morley finite element approximation. The first part establishes the well-posedness of the von Kármán obstacle problem and also discusses the uniqueness of the solution under an a priori and an a posteriori smallness condition on the data. The second part of the article discusses the regularity result of Frehse from 1971 and combines it with the regularity of the solution on a polygonal domain. The third part of the article shows an a priori error estimate for optimal convergence rates for the Morley finite element approximation to the von Kármán obstacle problem for small data. The article concludes with numerical results that illustrates the requirement of smallness assumption on the data for optimal convergence rate.
Keywords: Obstacle problem, Morley FEM, von Karman equations, a priori estimate, regularity
@article{M2AN_2021__55_5_1873_0,
author = {Carstensen, Carsten and Gaddam, Sharat and Nataraj, Neela and Pani, Amiya K. and Shylaja, Devika},
title = {Morley finite element method for the von {K\'arm\'an} obstacle problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1873--1894},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {5},
doi = {10.1051/m2an/2021042},
mrnumber = {4313374},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021042/}
}
TY - JOUR AU - Carstensen, Carsten AU - Gaddam, Sharat AU - Nataraj, Neela AU - Pani, Amiya K. AU - Shylaja, Devika TI - Morley finite element method for the von Kármán obstacle problem JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 1873 EP - 1894 VL - 55 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021042/ DO - 10.1051/m2an/2021042 LA - en ID - M2AN_2021__55_5_1873_0 ER -
%0 Journal Article %A Carstensen, Carsten %A Gaddam, Sharat %A Nataraj, Neela %A Pani, Amiya K. %A Shylaja, Devika %T Morley finite element method for the von Kármán obstacle problem %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 1873-1894 %V 55 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021042/ %R 10.1051/m2an/2021042 %G en %F M2AN_2021__55_5_1873_0
Carstensen, Carsten; Gaddam, Sharat; Nataraj, Neela; Pani, Amiya K.; Shylaja, Devika. Morley finite element method for the von Kármán obstacle problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 5, pp. 1873-1894. doi: 10.1051/m2an/2021042
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