A Nonconforming Finite Element Approximation for the von Karman Equations

TL;DR

This paper introduces a nonconforming finite element method for the von Karman equations, providing optimal error estimates and validating results through numerical experiments.

Contribution

It presents a novel nonconforming finite element approach with rigorous error analysis for the von Karman equations.

Findings

Optimal error estimates in broken energy and H^1 norms

Numerical results confirm theoretical error bounds

Method effectively models bending of thin elastic plates

Abstract

In this paper, a nonconforming finite element method has been proposed and analyzed for the von Karman equations that describe bending of thin elastic plates. Optimal order error estimates in broken energy and $H^1$ norms are derived under minimal regularity assumptions. Numerical results that justify the theoretical results are presented.