ENERGY CONSERVING GALERKIN FINITE ELEMENT METHODS FOR THE MAXWELL-KLEIN-GORDON SYSTEM

被引：6
|
作者：
Ma, Chupeng [1 ,2 ]
Cao, Liqun [3 ]
Lin, Yanping [4 ]
机构：
[1] Heidelberg Univ, Inst Appl Math, Neuenheimer Feld 205, D-69120 Heidelberg, Germany
[2] Heidelberg Univ, Interdisciplinary Ctr Sci Comp, Neuenheimer Feld 205, D-69120 Heidelberg, Germany
[3] Chinese Acad Sci, Univ Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci,LSEC,NCMIS, Beijing 100190, Peoples R China
[4] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2020年 / 58卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Maxwell-Klein-Gordon; energy conservation; finite element method; time integration scheme; error estimates; BACKWARD ERROR ANALYSIS; 2ND-ORDER SCHEME; EQUATION; CONVERGENCE;
D O I：
10.1137/17M1158690
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the Galerkin finite element methods for the Maxwell- Klein-Gordon system in the Coulomb gauge. We propose a semidiscrete finite element method for the system with the mixed finite element approximation of the vector potential. Energy conservation and error estimates are established for this scheme. A novel energy conserving time integration scheme is presented for solving the semidiscrete system. The existence and uniqueness of solutions to the fully discrete system are proved under some assumptions. Numerical experiments are carried out to support our theoretical analysis.
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页码：1339 / 1366
页数：28
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