Code generation for generally mapped finite elements
Abstract
Many classical finite elements such as the Argyris and Bell elements have long been absent from highlevel PDE software. Building on recent theoretical work, we describe how to implement very general finite element transformations in FInAT and hence into the Firedrake finite element system. Numerical results evaluate the new elements, comparing them to existing methods for classical problems. For a second order model problem, we find that new elements give smooth solutions at a mild increase in cost over standard Lagrange elements. For fourthorder problems, however, the newlyenabled methods significantly outperform interior penalty formulations. We also give some advanced use cases, solving the nonlinear CahnHilliard equation and some biharmonic eigenvalue problems (including Chladni plates) using $C^1$ discretizations.
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 arXiv:
 arXiv:1808.05513
 Bibcode:
 2018arXiv180805513K
 Keywords:

 Computer Science  Mathematical Software;
 Mathematics  Numerical Analysis
 EPrint:
 23 pages