The ultra weak variational formulation of thin clamped plate problems

We develop a new numerical scheme for a fourth order elliptic partial differential equation based on Kirchhoffʼs thin plate theory. In particular we extend the ultra weak variational formulation (UWVF) to thin plate problems with clamped plate boundary conditions. The UWVF uses a finite element mesh...

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Bibliographic Details
Published in:Journal of computational physics 2014-03, Vol.260, p.85-106
Main Authors: Luostari, Teemu, Huttunen, Tomi, Monk, Peter
Format: Article
Language:English
Subjects:
Boundaries
Clamped plate
Clamping
Convergence
Feasibility
Fourth order problem
Kirchhoffʼs thin plate
Mathematical analysis
Mathematical models
Non-polynomial
Norms
Thin plates
Ultra weak variational formulation
Upwind discontinuous Galerkin method
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Summary:We develop a new numerical scheme for a fourth order elliptic partial differential equation based on Kirchhoffʼs thin plate theory. In particular we extend the ultra weak variational formulation (UWVF) to thin plate problems with clamped plate boundary conditions. The UWVF uses a finite element mesh and non-polynomial basis functions. After deriving the new method we then prove L2 norm convergence on the boundary. Finally we investigate numerically the feasibility of the UWVF for both homogeneous and inhomogeneous problems and show examples of p- and h-convergence.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2013.12.028