Reports@SCM, Vol 5, No 1 (2020)

A Cº Interior Penalty Method for 4th order PDEs

Dani Fojo, David Codony, Sonia Fernandez-Mendez

Abstract


A method to solve 4th-order PDEs using the Finite Element Method (FEM) with standard Cº elements is derived and studied. It is based on a special weak form accounting for the discontinuous derivatives of the approximation and imposing their normal continuity across element sides in weak form. The method is developed for the equations of the deformation of a Kirchoff plate, but its extension to other 4th-order PDEs is expected to be straightforward. The accuracy and convergence of the resulting numerical approximation is studied with numerical experiments.

Keywords: 4th-order PDE, C0 Finite Elements, Nitsche's method, Interior Penalty Method.
MSC (2010): 35Q74, 74R10, 65M60.

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ISSN: 2385-4227 (electronic edition)