# Arbitrary high-order finite element schemes and high-order mass lumping

Sébastien Jund; Stéphanie Salmon

International Journal of Applied Mathematics and Computer Science (2007)

- Volume: 17, Issue: 3, page 375-393
- ISSN: 1641-876X

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topJund, Sébastien, and Salmon, Stéphanie. "Arbitrary high-order finite element schemes and high-order mass lumping." International Journal of Applied Mathematics and Computer Science 17.3 (2007): 375-393. <http://eudml.org/doc/207844>.

@article{Jund2007,

abstract = {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 Runge-Kutta scheme. We also construct in a systematic way a high-order quadrature which is optimal in terms of the number of points, which enables the use of mass lumping, up to P5 elements. We compare computational time and effort for several codes which are of high order in time and space and study their respective properties.},

author = {Jund, Sébastien, Salmon, Stéphanie},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {wave equation; finite element method; Cauchy-Kowalewski procedure; mass lumping; symbolic computation; higher order approximation},

language = {eng},

number = {3},

pages = {375-393},

title = {Arbitrary high-order finite element schemes and high-order mass lumping},

url = {http://eudml.org/doc/207844},

volume = {17},

year = {2007},

}

TY - JOUR

AU - Jund, Sébastien

AU - Salmon, Stéphanie

TI - Arbitrary high-order finite element schemes and high-order mass lumping

JO - International Journal of Applied Mathematics and Computer Science

PY - 2007

VL - 17

IS - 3

SP - 375

EP - 393

AB - 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 Runge-Kutta scheme. We also construct in a systematic way a high-order quadrature which is optimal in terms of the number of points, which enables the use of mass lumping, up to P5 elements. We compare computational time and effort for several codes which are of high order in time and space and study their respective properties.

LA - eng

KW - wave equation; finite element method; Cauchy-Kowalewski procedure; mass lumping; symbolic computation; higher order approximation

UR - http://eudml.org/doc/207844

ER -

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