New finite element methods in computational fluid dynamics by H(div) elements

被引：89
|
作者：
Wang, Junping
Ye, Xiu
机构：
[1] Natl Sci Fdn, Div Math Sci, Arlington, VA 22230 USA
[2] Univ Arkansas, Dept Math, Little Rock, AR 72204 USA
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2007年 / 45卷 / 03期
关键词：
finite element methods; Stokes problem; DISCONTINUOUS GALERKIN METHODS; NAVIER-STOKES EQUATIONS; ELLIPTIC PROBLEMS; SYSTEMS;
D O I：
10.1137/060649227
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the authors present two formulations for the Stokes problem which make use of the existing H(div) elements of the Raviart-Thomas type originally developed for the second-order elliptic problems. In addition, two new H(div) elements are constructed and analyzed particularly for the new formulations. Optimal-order error estimates are established for the corresponding finite element solutions in vaxious Sobolev norms. The finite element solutions feature a full satisfaction of the continuity equation when existing Raviart-Thomas-type elements are employed in the numerical scheme.
引用
收藏
页码：1269 / 1286
页数：18
相关论文
共 50 条
  • [41] Hierarchical high order finite element spaces in H(div, Ω) x H1(Ω) fora stabilized mixed formulation of Darcy problem
    Correa, Maicon R.
    Rodriguez, Juan C.
    Farias, Agnaldo M.
    de Siqueira, Denise
    Devloo, Philippe R. B.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 80 (05) : 1117 - 1141
  • [42] Novel spectral methods for shock capturing and the removal of tygers in computational fluid dynamics
    Kolluru, Sai Swetha Venkata
    Besse, Nicolas
    Pandit, Rahul
    JOURNAL OF COMPUTATIONAL PHYSICS, 2024, 519
  • [43] New H(div)-conforming multiscale hybrid-mixed methods for the elasticity problem on polygonal meshes
    Devloo, Philippe R. B.
    Farias, Agnaldo M.
    Gomes, Sonia M.
    Pereira, Weslley
    dos Santos, Antonio J. B.
    Valentin, Frederic
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2021, 55 (03): : 1005 - 1037
  • [44] New Mixed Finite Element Methods for Natural Convection with Phase-Change in Porous Media
    Alvarez, Mario
    Gatica, Gabriel N.
    Gomez-Vargas, Bryan
    Ruiz-Baier, Ricardo
    JOURNAL OF SCIENTIFIC COMPUTING, 2019, 80 (01) : 141 - 174
  • [45] NUMERICAL METHODS OF NEW MIXED FINITE ELEMENT SCHEME FOR SINGLE-PHASE COMPRESSIBLE FLOW
    Zhai, Shuying
    Feng, Xinlong
    Weng, Zhifeng
    INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2014, 11 (01)
  • [46] Developing computational methods for three-dimensional finite element simulations of coronary blood flow
    Kim, H. J.
    Vignon-Clementel, I. E.
    Figueroa, C. A.
    Jansen, K. E.
    Taylor, C. A.
    FINITE ELEMENTS IN ANALYSIS AND DESIGN, 2010, 46 (06) : 514 - 525
  • [47] A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements, Spectral Elements, and Discontinuous Galerkin
    Marras, Simone
    Kelly, James F.
    Moragues, Margarida
    Muller, Andreas
    Kopera, Michal A.
    Vazquez, Mariano
    Giraldo, Francis X.
    Houzeaux, Guillaume
    Jorba, Oriol
    ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING, 2016, 23 (04) : 673 - 722
  • [48] Mixed Discrete Element Method-Computational Fluid Dynamics Method applied to a Fire Extinguisher
    Coorevits, P.
    Marie, C.
    Benhabib, K.
    PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY, 2010, 94
  • [49] A matrix free, partitioned solution of fluid-structure interaction problems using finite volume and finite element methods
    Suliman, R.
    Oxtoby, O. F.
    Malan, A. G.
    Kok, S.
    EUROPEAN JOURNAL OF MECHANICS B-FLUIDS, 2015, 49 : 272 - 286
  • [50] ANISOTROPIC hp-ADAPTIVE DISCONTINUOUS GALERKIN FINITE ELEMENT METHODS FOR COMPRESSIBLE FLUID FLOWS
    Giani, Stefano
    Houston, Paul
    INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2012, 9 (04) : 928 - 949
12345