A C0 Interior Penalty Method for 4th order PDEs

Author (s): Fojo, D; Codony, D.; Fernández-Méndez, S.
Journal: reports@SCM

Volume: 5
Pages: 11 – 21
Date: 2020

A method to solve 4th-order PDEs using the Finite Element Method (FEM) with standard C0 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 straight-forward. The accuracy and convergence of the resulting numerical approximation is studied with numerical experiments.



  AUTHOR =       {Dani Fojo and David Codony and Fern{\'a}ndez-M{\'e}ndez, Sonia},
  TITLE =        {A C0 Interior Penalty Method for 4th order PDEs},
  JOURNAL =      {Reports@SCM},
  YEAR =         {2020},
  volume = {5},
  pages = {11--21},
  url = {http://revistes.iec.cat/index.php/reports/article/view/148126}