Geodesic
A balanced finite-element method for an axisymmetrically loaded thin shell
Applications of Mathematics, Tome 69 (2024) no. 2, pp. 151-168.

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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.
DOI : 10.21136/AM.2024.0134-23
Classification : 65N30, 74K25, 74S05
Keywords: axisymmetrically loaded thin shell; singular perturbation; balanced norm; layer-adapted meshes; finite element method 
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Heuer, Norbert; Linss, Torsten. A balanced finite-element method for an axisymmetrically loaded thin shell. Applications of Mathematics, Tome 69 (2024) no. 2, pp. 151-168. doi : 10.21136/AM.2024.0134-23. http://geodesic.mathdoc.fr/articles/10.21136/AM.2024.0134-23/

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