Morley Finite Element Method for the von K\'{a}rm\'{a}n Obstacle Problem
Abstract
This paper focusses on the von K\'{a}rm\'{a}n 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 K\'{a}rm\'{a}n 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 K\'{a}rm\'{a}n 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.
Cite
@article{arxiv.2009.03205,
title = {Morley Finite Element Method for the von K\'{a}rm\'{a}n Obstacle Problem},
author = {Carsten Carstensen and Sharat Gaddam and Neela Nataraj and Amiya K Pani and Devika Shylaja},
journal= {arXiv preprint arXiv:2009.03205},
year = {2020}
}
Comments
22 pages, 4 figures