scholarly journals Energy Conserving Explicit Local Time Stepping for Second-Order Wave Equations

2009 ◽  
Vol 31 (3) ◽  
pp. 1985-2014 ◽  
Author(s):  
Julien Diaz ◽  
Marcus J. Grote
Keyword(s):  
Local Time ◽  
Wave Equations ◽  
Second Order ◽  
Time Stepping ◽  
Local Time Stepping ◽  
Energy Conserving

scholarly journals Construction and convergence analysis of conservative second order local time discretisation for linear wave equations

2021 ◽  
Author(s):  
Juliette Chabassier ◽  
Sébastien Imperiale
Keyword(s):  
Local Time ◽  
Wave Equations ◽  
Second Order ◽  
Linear Wave ◽  
Time Step ◽  
Time Stepping ◽  
Time Discretisation ◽  
Regularity Properties ◽  
Local Time Stepping ◽  
Linear Wave Equations

In this work we present and analyse a time discretisation strategy for linear wave equations that aims at using locally in space the most adapted time discretisation among a family of implicit or explicit centered second order schemes. The proposed family of schemes is adapted to domain decomposition methods such as the mortar element method. They correspond in that case to local implicit schemes and to local time stepping. We show that, if some regularity properties of the solution are satisfied and if the time step verifies a stability condition, then the family of proposed time discretisations provides, in a strong norm, second order space-time convergence. Finally, we provide 1D and 2D numerical illustrations that confirm the obtained theoretical results and we compare our approach on 1D test cases to other existing local time stepping strategies for wave equations.

scholarly journals High order explicit local time stepping methods for hyperbolic conservation laws

2020 ◽  
Vol 89 (324) ◽  
pp. 1807-1842
Author(s):  
Thi-Thao-Phuong Hoang ◽  
Lili Ju ◽  
Wei Leng ◽  
Zhu Wang
Keyword(s):  
Conservation Laws ◽  
Local Time ◽  
Hyperbolic Conservation Laws ◽  
High Order ◽  
Hyperbolic Conservation ◽  
Time Stepping ◽  
Local Time Stepping

Time-accurate local time stepping method based on flux updating

AIAA Journal ◽  
1994 ◽  
Vol 32 (9) ◽  
pp. 1926-1929 ◽  
Author(s):  
X. D. Zhang ◽  
J.-Y. Trepanier ◽  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Local Time ◽  
Time Stepping ◽  
Local Time Stepping
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