Symbolic evaluation of hp-FEM element matrices on simplices
M.Sc. Tim HauboldNov. 20, 2018, 2:30 p.m. S2 054
In this talk we consider high-order finite element discretizations of linear elliptic boundary value problems. Following e.g. [Beuchler et al., 2012, Karniadakis, Sherwin] a set of hierarchic basis functions on simplices is chosen. For an affine 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 order 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 valued 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.