A balanced finite-element method for an axisymmetrically loaded thin shell

TL;DR

This paper develops and analyzes a finite-element method for thin shells under axisymmetric load, demonstrating robust convergence even as the shell thickness approaches zero, with numerical results confirming theoretical predictions.

Contribution

The paper introduces a balanced finite-element discretization that remains stable and convergent for thin shells with small thickness, addressing singular perturbation challenges.

Findings

Proves robust convergence of the method in a layer-sensitive norm.

Numerical experiments confirm theoretical convergence and stability.

Addresses singular perturbation issues in thin shell modeling.

Abstract

We analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the method in a balanced norm that captures the layers present in the solution. Numerical results confirm our findings.