Continuous piecewise linear finite elements for the Kirchhoff–Love plate equation
2012 (English)In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 121, no 1, 65-97 p.Article in journal (Refereed) Published
A family of continuous piecewise linear finite elements for thin plate problems is presented. We use standard linear interpolation of the deflection field to reconstruct a discontinuous piecewise quadratic deflection field. This allows us to use discontinuous Galerkin methods for the Kirchhoff–Love plate equation. Three example reconstructions of quadratic functions from linear interpolation triangles are presented: a reconstruction using Morley basis functions, a fully quadratic reconstruction, and a more general least squares approach to a fully quadratic reconstruction. The Morley reconstruction is shown to be equivalent to the basic plate triangle (BPT). Given a condition on the reconstruction operator, a priori error estimates are proved in energy norm and L2 norm. Numerical results indicate that the Morley reconstruction/BPT does not converge on unstructured meshes while the fully quadratic reconstruction show optimal convergence.
Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2012. Vol. 121, no 1, 65-97 p.
IdentifiersURN: urn:nbn:se:umu:diva-50810DOI: 10.1007/s00211-011-0429-5ISI: 000302749600003OAI: oai:DiVA.org:umu-50810DiVA: diva2:473342