Arbitrary high-order finite element schemes and high-order mass lumping
Sébastien Jund, Stéphanie Salmon (2007)
International Journal of Applied Mathematics and Computer Science
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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 elementsof 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...