Tim Haubold, Veronika Elisabeth Pillwein, Sven Beuchler,
"Recursion relations for hp-FEM Element Matrices on quadrilaterals"
, in Gesellschaft für Angewandte Mathematik und Mechanik (GAMM): Proceedings in Applied Mathematics and Mechanics (PAMM), Vol. 21, Nummer 1, Seite(n) e202100200--e2021002, 2021
Recursion relations for hp-FEM Element Matrices on quadrilaterals
Sprache des Titels:
Proceedings in Applied Mathematics and Mechanics (PAMM)
Abstract In this paper we consider higher order shape functions for finite elements on quadrilaterals. Using tensor products of suitable Jacobi polynomials, it can be proved that the corresponding mass and stiffness matrices are sparse with respect to polynomial degree p . Due to the orthogonal relations between Jacobi polynomials the exact values of the entries of mass and stiffness matrix can be determined. Using symbolic computation, we can find simple recurrence relations which allow us to compute the remaining nonzero entries in optimal arithmetic complexity. Besides the H1 case also the conformal basis functions for H(Div) and H(Curl) are investigated. conferencename: 91st Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)