scholarly journals Modified Galerkin Method for the Second Order Equation of Mixed Type and Estimate of Its Error

2016 ◽  
Vol 9 (4) ◽  
pp. 30-39 ◽  
Author(s):  
I.E. Egorov ◽  
◽  
V.E. Fedorov ◽  
I.M. Tikhonova ◽  
◽  
...  
Keyword(s):  
Galerkin Method ◽  
Mixed Type ◽  
Order Equation ◽  
Second Order ◽  
Equation Of Mixed Type

scholarly journals The Local Discontinuous Galerkin Method with Generalized Alternating Flux Applied to the Second-Order Wave Equations

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Rongpei Zhang ◽  
Jia Liu ◽  
Shaohua Jiang ◽  
Di Wang
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Wave Equations ◽  
Local Discontinuous Galerkin Method ◽  
Order Equation ◽  
Second Order ◽  
Local Discontinuous Galerkin ◽  
The Stability ◽  
The One

In this paper, we propose the local discontinuous Galerkin method based on the generalized alternating numerical flux for solving the one-dimensional second-order wave equation with the periodic boundary conditions. Introducing two auxiliary variables, the second-order equation is rewritten into the first-order equation systems. We prove the stability and energy conservation of this method. By virtue of the generalized Gauss–Radau projection, we can obtain the optimal convergence order in L2-norm of Ohk+1 with polynomial of degree k and grid size h. Numerical experiments are given to verify the theoretical results.

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