A $C^1$ Tetrahedral Finite Element without Edge Degrees of Freedom

Noel J. Walkington
2014 SIAM Journal on Numerical Analysis  
A composite C 1 tetrahedral finite element is developed which does not have any edge degrees of freedom. This eliminates the need to associate a basis for the planes perpendicular to each edge; such a basis can not depend continuously upon the edge orientation. The finite element space is piecewise polynomial over the four tetrahedra formed by adding the circumcenter, and their traces on each face belong to the (two dimensional) Bell subspace.
doi:10.1137/130912013 fatcat:w6pbdqfktvamdgp225bza2lxze