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

Norbert Heuer; Torsten Linss

Applications of Mathematics (2024)

  • Issue: 2, page 151-168
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Heuer, Norbert, and Linss, Torsten. "A balanced finite-element method for an axisymmetrically loaded thin shell." Applications of Mathematics (2024): 151-168. <http://eudml.org/doc/299279>.

@article{Heuer2024,
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.},
author = {Heuer, Norbert, Linss, Torsten},
journal = {Applications of Mathematics},
keywords = {axisymmetrically loaded thin shell; singular perturbation; balanced norm; layer-adapted meshes; finite element method},
language = {eng},
number = {2},
pages = {151-168},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A balanced finite-element method for an axisymmetrically loaded thin shell},
url = {http://eudml.org/doc/299279},
year = {2024},
}

TY - JOUR
AU - Heuer, Norbert
AU - Linss, Torsten
TI - A balanced finite-element method for an axisymmetrically loaded thin shell
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 2
SP - 151
EP - 168
AB - 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.
LA - eng
KW - axisymmetrically loaded thin shell; singular perturbation; balanced norm; layer-adapted meshes; finite element method
UR - http://eudml.org/doc/299279
ER -

References

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