A finite element method by patch reconstruction for the Stokes problem using mixed formulations

被引：11
作者：
Li, Ruo [1 ,2 ]
Sun, Zhiyuan [3 ]
Yang, Fanyi [3 ]
Yang, Zhijian [4 ]
机构：
[1] Peking Univ, LMAM, CAPT, Beijing 100871, Peoples R China
[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
[3] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
[4] Wuhan Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 353卷
关键词：
Stokes problem; Reconstructed basis function; Discontinuous Galerkin method; inf-sup test; DISCONTINUOUS GALERKIN METHODS; PART I; HYBRIDIZATION; SYSTEM;
D O I：
10.1016/j.cam.2018.12.017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we develop a patch reconstruction finite element method for the Stokes problem. The weak formulation of the interior penalty discontinuous Galerkin is employed. The proposed method has a great flexibility in velocity-pressure space pairs whose stability properties are confirmed by the inf-sup tests. Numerical examples show the applicability and efficiency of the proposed method. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：1 / 20
页数：20
相关论文
共 34 条
[1]   hp-VERSION COMPOSITE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS ON COMPLICATED DOMAINS [J].
Antonietti, Paola F. ;
Giani, Stefano ;
Houston, Paul .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2013, 35 (03) :A1417-A1439
[2]   Unified analysis of discontinuous Galerkin methods for elliptic problems [J].
Arnold, DN ;
Brezzi, F ;
Cockburn, B ;
Marini, LD .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (05) :1749-1779
[3]   AN INTERIOR PENALTY FINITE-ELEMENT METHOD WITH DISCONTINUOUS ELEMENTS [J].
ARNOLD, DN .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1982, 19 (04) :742-760
[4]   PIECEWISE SOLENOIDAL VECTOR-FIELDS AND THE STOKES PROBLEM [J].
BAKER, GA ;
JUREIDINI, WN ;
KARAKASHIAN, OA .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1990, 27 (06) :1466-1485
[5]   An inf-sup test for shell finite elements [J].
Bathe, KJ ;
Iosilevich, A ;
Chapelle, D .
COMPUTERS & STRUCTURES, 2000, 75 (05) :439-456
[6]  
Beirao da Veiga L., 2014, MS A MODELING SIMULA, DOI [10.1007/978-3-319-02663-3, DOI 10.1007/978-3-319-02663-3]
[7]  
BOFFI D., 2013, SPRINGER SER COMPUT, V44, DOI [10.1007/978-3-642-36519-5, DOI 10.1007/978-3-642-36519-5]
[8]   MIMETIC FINITE DIFFERENCES FOR ELLIPTIC PROBLEMS [J].
Brezzi, Franco ;
Buffa, Annalisa ;
Lipnikov, Konstantin .
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2009, 43 (02) :277-295
[9]  
Carrero J, 2006, MATH COMPUT, V75, P533, DOI 10.1090/S0025-5718-05-01804-1
[10]   THE INF-SUP TEST [J].
CHAPELLE, D ;
BATHE, KJ .
COMPUTERS & STRUCTURES, 1993, 47 (4-5) :537-545
1234