# Symbolic evaluation of hp-FEM element matrices on simplices

## M.Sc. Tim Haubold

Nov. 20, 2018, 3:30 p.m. S2 054

In this talk we consider high-order finite element discretizations of linear ellip-
tic boundary value problems. Following e.g. [Beuchler et al., 2012, Karniadakis,
Sherwin] a set of hierarchic basis functions on simplices is chosen. For an affine
simplicial triangulation this leads to a sparse stiffness matrix. Moreover the L2-inner
product of the interior basis functions is sparse with respect to the polynomial or-
der p. The construction relies on a tensor-product based construction with properly
weighted Jacobi polynomials.
In this talk we give an outlook in the computation of the remaining non zero entries
of mass and stiffness matrix. To obtain this, recursion fomulas based on symbolic
methods will be used. The aim of this technique lies in the application to vector va-
lued problems in H(div) and H(curl), where an explict splitting of the higher-order
basic functions into solenoidal and non-solenoidal ones is used.