A Stabilized Finite Volume Element Method for Stationary Stokes-Darcy Equations Using the Lowest Order

被引：3
|
作者：
Wu, Yanyun [1 ]
Mei, Liquan [2 ]
Qiu, Meilan [3 ]
Chu, Yuchuan [4 ]
机构：
[1] Chongqing Univ Posts & Telecommun, Sch Sci, Chongqing 400065, Peoples R China
[2] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China
[3] Huizhou Univ, Sch Math & Big Data, Huizhou 516007, Guangdong, Peoples R China
[4] Dongguan Univ Technol, Sch Mech Engn, Dongguan 523808, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS | 2020年 / 17卷 / 08期
关键词：
Finite volume element method; Stokes-Darcy equation; stabilized method; error estimation; local mass conservation; DISCONTINUOUS GALERKIN METHODS;
D O I：
10.1142/S0219876219500531
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
We present a stabilized finite volume element method for the coupled Stokes-Darcy problem with the lowest order P-1 - P-0 element for the Stokes region and Pi element for the Darcy region. Based on adding a jump term of discrete pressure to the approximation equation, a discrete inf-sup condition is established for the proposed method. The optimal error estimates in the H-1-norm for the velocity and piezometric head and in the L-2-norm for the pressure are proved. And they are also verified through some numerical experiments. Two figures are given to show the full comparison for the local mass conservation between the proposed method and the stabilized finite element method. And this method can also be computed directly in the irregular domain according to the last experiment.
引用
收藏
页数：28
相关论文
共 50 条
  • [1] Stabilized finite element method for the stationary mixed Stokes-Darcy problem
    Yu, Jiaping
    Al Mahbub, Md Abdullah
    Shi, Feng
    Zheng, Haibiao
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2018,
  • [2] A stabilized finite volume element method for a coupled Stokes-Darcy problem
    Li, Rui
    Li, Jian
    He, Xiaoming
    Chen, Zhangxin
    [J]. APPLIED NUMERICAL MATHEMATICS, 2018, 133 : 2 - 24
  • [3] A stabilized finite volume method for the evolutionary Stokes-Darcy system
    Li, Yi
    Hou, Yanren
    Li, Rui
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 75 (02) : 596 - 613
  • [4] An adaptive stabilized finite element method for the Stokes-Darcy coupled problem
    Araya, Rodolfo
    Carcamo, Cristian
    Poza, Abner H.
    Vino, Eduardo
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 443
  • [5] Discontinuous Finite Volume Element Method for a Coupled Non-stationary Stokes-Darcy Problem
    Li, Rui
    Gao, Yali
    Li, Jian
    Chen, Zhangxin
    [J]. JOURNAL OF SCIENTIFIC COMPUTING, 2018, 74 (02) : 693 - 727
  • [6] Local and Parallel Stabilized Finite Element Methods Based on the Lowest Equal-Order Elements for the Stokes-Darcy Model
    Han, Jing
    Du, Guangzhi
    [J]. MATHEMATICS, 2023, 11 (23)
  • [7] A stabilized finite volume method for Stokes equations using the lowest order P 1 - P 0 element pair
    Zhang, Tie
    Tang, Lixin
    [J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2015, 41 (04) : 781 - 798
  • [8] Discontinuous finite volume methods for the stationary Stokes-Darcy problem
    Wang, Gang
    He, Yinnian
    Li, Rui
    [J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2016, 107 (05) : 395 - 418
  • [9] A UNIFIED STABILIZED FINITE VOLUME METHOD FOR STOKES AND DARCY EQUATIONS
    Boukabache, Akram
    Kechkar, Nasserdine
    [J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2019, 56 (04) : 1083 - 1112
  • [10] Stabilized finite element method for the stationary mixed Stokes–Darcy problem
    Jiaping Yu
    Md. Abdullah Al Mahbub
    Feng Shi
    Haibiao Zheng
    [J]. Advances in Difference Equations, 2018
12345