Convergence of a space-time continuous Galerkin method for the wave equation

被引：1
|
作者：
Zhao, Zhihui [1 ]
Li, Hong [1 ]
机构：
[1] Inner Mongolia Univ, Sch Math Sci, 235 West Rd Univ, Saihan Dist 010021, Hohhot, Peoples R China
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2016年
基金：
美国国家科学基金会;
关键词：
continuous Galerkin method; wave equation; optimal orders of convergence; numerical example; CONTINUOUS FINITE-ELEMENTS;
D O I：
10.1186/s13660-016-1215-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper gives a new theoretical analysis of the space-time continuous Galerkin (STCG) method for the wave equation. We prove the existence and uniqueness of the numerical solutions and get optimal orders of convergence to numerical solutions regarding space that do not need any compatibility conditions on the space and time mesh size. Finally, we employ a numerical example to validate the effectiveness and feasibility of the STCG method.
引用
收藏
页数：18
相关论文
共 50 条
  • [41] ON THE CONVERGENCE OF SPACE-TIME DISCONTINUOUS GALERKIN SCHEMES FOR SCALAR CONSERVATION LAWS
    May, Georg
    Zakerzadeh, Mohammad
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2016, 54 (04) : 2452 - 2465
  • [42] STABILITY OF ALE SPACE-TIME DISCONTINUOUS GALERKIN METHOD
    Vlasak, Miloslav
    Balazsova, Monika
    Feistauer, Miloslav
    [J]. PROCEEDINGS OF EQUADIFF 2017 CONFERENCE, 2017, : 237 - 246
  • [43] Comparison of Newmark and space-time discontinuous Galerkin method
    Aksoy, HG
    Tanröver, H
    Senocak, E
    [J]. ENGINEERING, CONSTRUCTION AND OPERATIONS IN CHALLENGING ENVIRONMENTS: EARTH AND SPACE 2004, 2004, : 532 - 539
  • [44] Space-time discontinuous Galerkin method for linear elastodynamics
    Aksoy, H. G.
    Senocak, E.
    [J]. JOURNAL OF AEROSPACE ENGINEERING, 2007, 20 (02) : 128 - 131
  • [45] CONGRUENCE CONVERGENCE IN PP-WAVE SPACE-TIME
    Fathi, M.
    Mohseni, M.
    [J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2018, 195 (02) : 729 - 744
  • [46] A fast Galerkin finite element method for a space-time fractional Allen-Cahn equation
    Liu, Huan
    Cheng, Aijie
    Wang, Hong
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 368
  • [47] Variational space-time (dis)continuous Galerkin method for nonlinear free surface water waves
    Gagarina, E.
    Ambati, V. R.
    van der Vegt, J. J. W.
    Bokhove, O.
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 275 : 459 - 483
  • [48] Elastic Wave Propagation Analysis Using the Space-Time Discontinuous Galerkin Quadrature Element Method
    Liao, Minmao
    Wei, Jie
    Zhao, Jiaze
    Fan, Wensu
    [J]. JOURNAL OF ENGINEERING MECHANICS, 2024, 150 (10)
  • [49] A space-time fully decoupled wavelet Galerkin method for solving a class of nonlinear wave problems
    Liu, Xiaojing
    Wang, Jizeng
    Zhou, Youhe
    [J]. NONLINEAR DYNAMICS, 2017, 90 (01) : 599 - 616
  • [50] A high-order space-time ultra-weak discontinuous Galerkin method for the second-order wave equation in one space dimension
    Baccouch, Mahboub
    Temimi, Helmi
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2021, 389
12345