Volume 55, Number 5, September-October 2021
|Page(s)||1873 - 1894|
|Published online||17 September 2021|
Morley finite element method for the von Kármán obstacle problem
Department of Mathematics, HU Berlin, Berlin 10099, Germany
2 Distinguished Visiting Professor, Department of Mathematics, IIT Bombay, Powai, Mumbai 400076 India
3 Department of Mathematics, IIT Bombay, Powai, Mumbai 400076, India
4 IITB-Monash Research Academy, IIT Bombay, Powai, Mumbai 400076 India
* Corresponding author: firstname.lastname@example.org
Accepted: 2 August 2021
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.
Mathematics Subject Classification: 65K15 / 65N12 / 65N15 / 65N30
Key words: Obstacle problem / Morley FEM / von Karman equations / a priori estimate / regularity
© The authors. Published by EDP Sciences, SMAI 2021
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