Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation

2001 ◽  
Vol 38 (6) ◽  
pp. 2047-2078 ◽  
Author(s):  
G. Cohen ◽  
P. Joly ◽  
J. E. Roberts ◽  
N. Tordjman
Keyword(s):  
Wave Equation ◽  
Finite Elements ◽  
Higher Order ◽  
Mass Lumping ◽  
Triangular Finite Elements

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.

scholarly journals Higher Order Cut Finite Elements for the Wave Equation

2019 ◽  
Vol 80 (3) ◽  
pp. 1867-1887 ◽  
Author(s):  
Simon Sticko ◽  
Gunilla Kreiss
Keyword(s):  
Wave Equation ◽  
Finite Elements ◽  
Higher Order

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

Sign in / Sign up

Export Citation Format

Share Document