TY - JOUR
T1 - A conservative Galerkin finite element method for the Klein- Gordon equation in high dimensions
AU - Huawei Zhao and Yue Cheng
JO - Journal of Information and Computing Science
VL - 3
SP - 170
EP - 175
PY - 2024
DA - 2024/01
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22409.html
KW - Klein-Gordon equation, Energy conservation, Galerkin FEM 

AB - School of Mathematics and Statistics, Nanjing University of Information Science & Technology,  
Nanjing, 210044, China 
(Received January 06 2019, accepted May 20 2019) 
 In  this  article,  we  design  and  analyze  a  Galerkin  finite  element  method  (FEM)  to  solve  the 
nonlinear Klein-Gordon equation in ?(? = 1,2,3) dimensions. The scheme is proved to preserve well the total 
energy  in  the  discrete  sense,  which  is  consistent  with  the  conservative  property  possessed  by  the  original  
problem. Numerical results are reported to show the high accuracy of the numerical methods and confirm the 
energy conservation.