A note on the numerical dissipation from high-order discontinuous finite element schemes

2014 ◽  
Vol 98 ◽  
pp. 186-195 ◽  
Author(s):  
Antony Jameson ◽  
Guido Lodato
Keyword(s):  
Finite Element ◽  
High Order ◽  
Numerical Dissipation ◽  
Discontinuous Finite Element ◽  
Finite Element Schemes

scholarly journals High‐order space‐time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling

2014 ◽  
Vol 98 (2) ◽  
pp. 131-156 ◽  
Author(s):  
H. T. Banks ◽  
Malcolm J Birch ◽  
Mark P Brewin ◽  
Stephen E Greenwald ◽  
Shuhua Hu ◽  
...  
Keyword(s):  
Finite Element ◽  
Wave Equations ◽  
Space Time ◽  
High Order ◽  
Finite Element Schemes

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 Interpolation Hermite Polynomials For Finite Element Method

2018 ◽  
Vol 173 ◽  
pp. 03009 ◽  
Author(s):  
Alexander Gusev ◽  
Sergue Vinitsky ◽  
Ochbadrakh Chuluunbaatar ◽  
Galmandakh Chuluunbaatar ◽  
Vladimir Gerdt ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hermite Interpolation ◽  
Hermite Polynomials ◽  
High Accuracy ◽  
High Order ◽  
Analytic Calculation ◽  
Interpolation Polynomials ◽  
Finite Element Schemes ◽  
Hermite Interpolation Polynomials

We describe a new algorithm for analytic calculation of high-order Hermite interpolation polynomials of the simplex and give their classification. A typical example of triangle element, to be built in high accuracy finite element schemes, is given.

Sign in / Sign up

Export Citation Format

Share Document