scholarly journals Continuous finite elements in space and time for the nonhomogeneous wave equation

1994 ◽  
Vol 27 (3) ◽  
pp. 91-102 ◽  
Author(s):  
L. Bales ◽  
I. Lasiecka
Keyword(s):  
Wave Equation ◽  
Finite Elements ◽  
Space And Time

Finite elements in space and time for dynamic contact problems

2008 ◽  
Vol 76 (10) ◽  
pp. 1632-1644 ◽  
Author(s):  
H. Blum ◽  
T. Jansen ◽  
A. Rademacher ◽  
K. Weinert
Keyword(s):  
Finite Elements ◽  
Contact Problems ◽  
Dynamic Contact ◽  
Space And Time

scholarly journals Arbitrary High-Order Finite Element Schemes and High-Order Mass Lumping

2007 ◽  
Vol 17 (3) ◽  
pp. 375-393 ◽  
Author(s):  
Sébastien Jund ◽  
Stéphanie Salmon
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Finite Elements ◽  
Taylor Expansion ◽  
High Order ◽  
Computational Time ◽  
Mass Lumping ◽  
Stiffness Matrices ◽  
High Order Time ◽  
Finite Element Schemes

Arbitrary High-Order Finite Element Schemes and High-Order Mass LumpingComputers 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 orderkand 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 toP5elements. We compare computational time and effort for several codes which are of high order in time and space and study their respective properties.

Sign in / Sign up

Export Citation Format

Share Document