On Efficient Solution of Linear Systems Arising in hp-FEM

Abstract

This contribution studies the static condensation of internal degrees of freedom which allows for efficient solution of linear algebraic systems arising in higher-order finite element methods. On each element, the static condensation eliminates the degrees of freedom corresponding to the internal (or bubble) basis functions. The elimination is local in elements and can be done in parallel. The resulting Schur complement system is considerably smaller and, moreover, it has less nonzero elements and better condition number in comparison with the original system. This paper focuses on the numerical performace of the static condensation and shows its CPU time efficiency.