A symmetric mixed covolume method for the nonlinear parabolic problem

被引：0
作者：
Zhao, Xuan [1 ]
Liu, Zhengguang [2 ,3 ,4 ]
机构：
[1] Shandong Univ, Sch Math, Jinan, Peoples R China
[2] Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan, Peoples R China
[3] Sch Math & Computat Sci, Xiangtan, Peoples R China
[4] Shandong Normal Univ, Sch Math & Stat, Jinan, Peoples R China
来源：
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2022年 / 68卷 / 03期
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
Symmetric mixed covolume method; Rectangular grids; Existence and uniqueness; Nonlinear parabolic problem; Error estimates; FINITE-ELEMENT METHODS; SUPERCONVERGENCE; EQUATION; GRIDS;
D O I：
10.1007/s12190-021-01582-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we develop a symmetric mixed covolume scheme for the nonlinear parabolic equations. The existence and uniqueness of the scheme are proved by using the lowest order Raviart-Thomas mixed element space on rectangular grids. We carry out a rigorous error estimates for the constructed scheme, establishing the first-order convergence for both velocity and pressure. Numerical examples are provided to verify that the numerical results are all in consistent with the theoretical analysis.
引用
收藏
页码：1591 / 1611
页数：21
相关论文
共 29 条
  • [1] Adams RA., 2003, SOBOLEV SPACES, P713
  • [2] Optimal Control for a Groundwater Pollution Ruled by a Convection-Diffusion-Reaction Problem
    Augeraud-Veron, Emmanuelle
    Choquet, Catherine
    Comte, Eloise
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2017, 173 (03) : 941 - 966
  • [3] Superconvergence of mixed covolume method for elliptic problems on triangular grids
    Bi, Chunjia
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 216 (02) : 534 - 544
  • [4] Chatzipantelidis P., 2013, SPRINGER P MATH STAT, V45, P121
  • [5] A two-grid MMOC finite element method for nonlinear variable-order time-fractional mobile immobile advection-diffusion equations
    Chen, Chuanjun
    Liu, Huan
    Zheng, Xiangcheng
    Wang, Hong
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 79 (09) : 2771 - 2783
  • [6] A two-grid finite element method for nonlinear parabolic integro-differential equations
    Chen, Chuanjun
    Zhang, Xiaoyan
    Zhang, Guodong
    Zhang, Yuanyuan
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2019, 96 (10) : 2010 - 2023
  • [7] Two-grid methods for finite volume element approximations of nonlinear parabolic equations
    Chen, Chuanjun
    Yang, Min
    Bi, Chunjia
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 228 (01) : 123 - 132
  • [8] Mixed covolume methods on rectangular grids for elliptic problems
    Chou, SH
    Kwak, DY
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2000, 37 (03) : 758 - 771
  • [9] Govindarajan Suresh Kumar, 2018, Groundwater for Sustainable Development, V7, P56, DOI 10.1016/j.gsd.2018.03.006
  • [10] Mixed finite element domain decomposition for nonlinear parabolic problems
    Kim, MY
    Park, EJ
    Park, J
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2000, 40 (8-9) : 1061 - 1070
123