CONSERVATION SCHEMES FOR CONVECTION-DIFFUSION EQUATIONS WITH ROBIN BOUNDARY CONDITIONS

被引：4
|
作者：
Flotron, Stephane [1 ]
Rappaz, Jacques [1 ]
机构：
[1] Ecole Polytech Fed Lausanne, CH-1015 Lausanne, Switzerland
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2013年 / 47卷 / 06期
关键词：
Finite Elements; numerical conservation schemes; Robin boundary condition; convection-diffusion equations;
D O I：
10.1051/m2an/2013087
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we present a numerical scheme based on a finite element method in order to solve a time-dependent convection-diffusion equation problem and satisfy some conservation properties. In particular, our scheme is able to conserve the total energy for a heat equation or the total mass of a solute in a fluid for a concentration equation, even if the approximation of the velocity field is not completely divergence-free. We establish a priori errror estimates for this scheme and we give some numerical examples which show the efficiency of the method.
引用
收藏
页码：1765 / 1781
页数：17
相关论文
共 50 条
  • [1] A simple and efficient curved boundary scheme of the lattice Boltzmann method for Robin boundary conditions of convection-diffusion equations
    Xie, Xinyuan
    Zhao, Weifeng
    Lin, Ping
    APPLIED MATHEMATICS LETTERS, 2021, 122
  • [2] Highly Accurate Method for a Singularly Perturbed Coupled System of Convection-Diffusion Equations with Robin Boundary Conditions
    Ahmed, H. M.
    JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2024, 31 (01)
  • [3] On the uniqueness of linear convection-diffusion equations with integral boundary conditions
    Lee, Chiun-Chang
    Mizuno, Masashi
    Moon, Sang-Hyuck
    COMPTES RENDUS MATHEMATIQUE, 2023, 361 (01) : 191 - 206
  • [4] Analysis of a singular limit of boundary conditions for convection-diffusion equations
    Chacon Rebollo, Tomas
    Gomez Marmol, Macarena
    Sanchez Munoz, Isabel
    ASYMPTOTIC ANALYSIS, 2010, 70 (3-4) : 141 - 154
  • [5] Boundary conditions of the lattice Boltzmann method for convection-diffusion equations
    Huang, Juntao
    Yong, Wen-An
    JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 300 : 70 - 91
  • [6] DEGENERATE CONVECTION-DIFFUSION EQUATION WITH A ROBIN BOUNDARY CONDITION
    Karimou, Mohamed Gazibo
    HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS, 2014, 8 : 583 - 590
  • [7] LINEARLY IMPLICIT SCHEMES FOR CONVECTION-DIFFUSION EQUATIONS
    Cavalli, Fausto
    HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS, 2014, 8 : 423 - 430
  • [8] A new unconditionally stable explicit scheme for the convection-diffusion equation with Robin boundary conditions
    Xie, Zhihua
    Lin, Jianguo
    Zhou, Juntao
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2008, 85 (12) : 1833 - 1847
  • [9] Half boundary method for steady state convection-diffusion equations with different boundary conditions
    Zhao, Yuanyuan
    Huang, Mei
    Ouyang, Xiaoping
    Tang, Jiannan
    Morita, Chihiro
    ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2020, 113 : 26 - 39
  • [10] ENTROPY STABLE SCHEMES FOR DEGENERATE CONVECTION-DIFFUSION EQUATIONS
    Jerez, Silvia
    Pares, Carlos
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2017, 55 (01) : 240 - 264
12345