The ultra weak variational formulation of thin clamped plate problems

Authors:
Teemu Luostari;Tomi Huttunen;Peter Monk
Affiliations:
Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland;Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland;Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
Venue:
Journal of Computational Physics
Year:
2014

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Abstract

We develop a new numerical scheme for a fourth order elliptic partial differential equation based on Kirchhoff@?s 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 L^2 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.