# Direct Field Problems: Sparse high-order shape functions for $H$(curl) and $H$(div)

## Priv.-Doz. Dr. Sven Beuchler

Dec. 12, 2008, 1 p.m. HF 136

In this talk, we construct high order polynomial functions on triangular and tetrahedral meshes in $H$(curl) and $H$(div).

We prove that the presented basis functions form a orthogonal system. In $H$(curl), the orthogonality of all basis functions to each other is shown for the 2D case. In the 3D-case, all basis functions are orthogonal to most of the other basis functions. The proofs requires Mathematica packages which are derived by Veronika Pillwein.