scholarly journals High-Order Time Integration in the p-Version of Finite Elements

PAMM ◽  
2010 ◽  
Vol 10 (1) ◽  
pp. 201-202
Author(s):  
Torben Netz ◽  
Stefan Hartmann
Keyword(s):  
Finite Elements ◽  
Time Integration ◽  
High Order ◽  
High Order Time

Simulating the temporal change of the active response of arteries by finite elements with high-order time-integrators

2019 ◽  
Vol 64 (6) ◽  
pp. 1669-1684 ◽  
Author(s):  
Rose Rogin Gilbert ◽  
Matthias Grafenhorst ◽  
Stefan Hartmann ◽  
Zohar Yosibash
Keyword(s):  
Finite Elements ◽  
Temporal Change ◽  
High Order ◽  
Active Response ◽  
Time Integrators ◽  
High Order 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.

scholarly journals Conservative High-Order Time Integration for Lagrangian Hydrodynamics

2021 ◽  
Vol 43 (1) ◽  
pp. A221-A241
Author(s):  
Adrian Sandu ◽  
Vladimir Tomov ◽  
Lenka Cervena ◽  
Tzanio Kolev
Keyword(s):  
Time Integration ◽  
High Order ◽  
Lagrangian Hydrodynamics ◽  
High Order Time
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