A Discontinuous Finite Volume Element Method Based on Bilinear Trial Functions

被引:1
作者
Zhang, Tie [1 ]
Tang, Lixin [2 ]
机构
[1] Northeastern Univ, Dept Math, Res Ctr Natl Met Automat, Shenyang 110004, Peoples R China
[2] Northeastern Univ, State Key Lab Synthet Automat Proc Ind, Res Ctr Natl Met Automat, Shenyang 110004, Peoples R China
关键词
Discontinuous finite volume element; bilinear trial function; optimal error estimate; elliptic and parabolic problems; UNIFIED ANALYSIS; CONVERGENCE; SCHEMES;
D O I
10.1142/S0219876217500256
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We propose a discontinuous finite volume element (DFVE) method for second order elliptic and parabolic problems. Discontinuous bilinear functions are used as the trial functions. We give the stability analysis of this DFVE method and derive the optimal error estimates in the broken H-1- norm. Specifically, the optimal L-2- error is obtained for the first time for the bilinear DFVE methods solving elliptic and parabolic problems.
引用
收藏
页数:21
相关论文
共 50 条
  • [41] Flux reconstruction using Jacobi correction functions in discontinuous spectral element method
    Peyvan, Ahmad
    Komperda, Jonathan
    Li, Dongru
    Ghiasi, Zia
    Mashayek, Farzad
    JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 435
  • [42] Adaptive Bilinear Element Finite Volume Methods for Second-Order Elliptic Problems on Nonmatching Grids
    Chen, Yanli
    Li, Yonghai
    Sheng, Zhiqiang
    Yuan, Guangwei
    JOURNAL OF SCIENTIFIC COMPUTING, 2015, 64 (01) : 130 - 150
  • [43] Discontinuous Galerkin Finite Volume Element Methods for Second-Order Linear Elliptic Problems
    Kumar, Sarvesh
    Nataraj, Neela
    Pani, Amiya K.
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2009, 25 (06) : 1402 - 1424
  • [44] Mixed and discontinuous finite volume element schemes for the optimal control of immiscible flow in porous media
    Kumar, Sarvesh
    Ruiz-Baier, Ricardo
    Sandilya, Ruchi
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 76 (04) : 923 - 937
  • [45] Mixed Integration Scheme for Embedded Discontinuous Interfaces by Extended Finite Element Method
    Yu, Peng
    Hao, Qingshuo
    Wang, Xiangnan
    Yu, Yuzhen
    Zhan, Zhenggang
    FRONTIERS IN EARTH SCIENCE, 2022, 9
  • [46] An asynchronous spacetime discontinuous Galerkin finite element method for time domain electromagnetics
    Abedi, Reza
    Mudaliar, Saba
    JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 351 : 121 - 144
  • [47] A polygonal finite volume element method for anisotropic diffusion problems
    Zhou, Yanhui
    Zhang, Yanlong
    Wu, Jiming
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2023, 140 : 225 - 236
  • [48] Biquadratic element discrete duality finite volume method for on mesh
    Pan, Kejia
    Wu, Xiaoxin
    Xu, Yufeng
    JOURNAL OF COMPUTATIONAL PHYSICS, 2024, 503
  • [49] An analysis of finite volume element method for solving the Signorini problem
    Zhang, Tie
    Li, Zheng
    APPLIED MATHEMATICS AND COMPUTATION, 2015, 270 : 830 - 841
  • [50] A new combined finite element-upwind finite volume method for convection-dominated diffusion problems
    Wang, Cheng
    He, Mingyan
    Sun, Pengtao
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2016, 32 (03) : 799 - 818