A balanced finite-element method for an axisymmetrically loaded thin shell. (English) Zbl 07893329
Summary: 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.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 74K25 | Shells |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
axisymmetrically loaded thin shell; singular perturbation; balanced norm; layer-adapted meshes; finite element methodReferences:
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