Arbitrary high-order finite element schemes and high-order mass lumping - Jund, Sébastien; Salmon, Stéphanie (Zielona Góra: Uniwersytet Zielonogórski)
Computers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elements of order k and show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit Runge-Kutta scheme.
Keywords: wave equation; Finite Element Method (FEM); mass lumping; Cauchy-Kowalewski procedure