Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier-Stokes equations

被引：3
|
作者：
Masri, Rami [1 ]
Liu, Chen [2 ]
Riviere, Beatrice [3 ]
机构：
[1] Simula Res Lab, Dept Numer Anal & Sci Comp, Oslo, Norway
[2] Purdue Univ, Dept Math, W Lafayette, IN USA
[3] Rice Univ, Dept Computat & Appl Math, Houston, TX 77005 USA
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 39卷 / 04期
基金：
美国国家科学基金会;
关键词：
discontinuous Galerkin; operator splitting; time-dependent Navier-Stokes; PROJECTION METHODS; SPLITTING METHOD; APPROXIMATION; CONVERGENCE;
D O I：
10.1002/num.23002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The pressure correction scheme is combined with interior penalty discontinuous Galerkin method to solve the time-dependent Navier-Stokes equations. Optimal error estimates are derived for the velocity in the L-2 norm in time and in space. Error bounds for the discrete time derivative of the velocity and for the pressure are also established. The analysis is challenging and technical and is based on appropriate use of lift operators and duality arguments.
引用
收藏
页码：3108 / 3144
页数：37
相关论文
共 50 条
  • [1] A priori error estimates of a discontinuous Galerkin method for the Navier-Stokes equations
    Saumya Bajpai
    Deepjyoti Goswami
    Kallol Ray
    Numerical Algorithms, 2023, 94 : 937 - 1002
  • [2] A priori error estimates of a discontinuous Galerkin method for the Navier-Stokes equations
    Bajpai, Saumya
    Goswami, Deepjyoti
    Ray, Kallol
    NUMERICAL ALGORITHMS, 2023, 94 (02) : 937 - 1002
  • [3] A DISCONTINUOUS GALERKIN PRESSURE CORRECTION SCHEME FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS: STABILITY AND CONVERGENCE
    Masri, Rami
    Liu, Chen
    Riviere, Beatrice
    MATHEMATICS OF COMPUTATION, 2022, 91 (336) : 1625 - 1654
  • [4] ERROR ESTIMATES OF A STABILIZED LAGRANGE-GALERKIN SCHEME FOR THE NAVIER-STOKES EQUATIONS
    Notsu, Hirofumi
    Tabata, Masahisa
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2016, 50 (02): : 361 - 380
  • [5] DISCONTINUOUS GALERKIN APPROXIMATIONS OF THE STOKES AND NAVIER-STOKES EQUATIONS
    Chrysafinos, Konstantinos
    Walkington, Noel J.
    MATHEMATICS OF COMPUTATION, 2010, 79 (272) : 2135 - 2167
  • [6] A discontinuous Galerkin method for the Navier-Stokes equations
    Lomtev, I
    Karniadakis, GE
    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 1999, 29 (05) : 587 - 603
  • [7] AN EXACTLY COMPUTABLE LAGRANGE-GALERKIN SCHEME FOR THE NAVIER-STOKES EQUATIONS AND ITS ERROR ESTIMATES
    Tabata, Masahisa
    Uchiumi, Shinya
    MATHEMATICS OF COMPUTATION, 2018, 87 (309) : 39 - 67
  • [8] Central Discontinuous Galerkin Method for the Navier-Stokes Equations
    Tan Ren
    Chao Wang
    Haining Dong
    Danjie Zhou
    Journal of Beijing Institute of Technology, 2017, 26 (02) : 158 - 164
  • [9] Discontinuous Galerkin schemes for the compressible Navier-Stokes equations
    Drozo, C
    Borrel, M
    Lerat, A
    SIXTEENTH INTERNATIONAL CONFERENCE ON NUMERICAL METHODS IN FLUID DYNAMICS, 1998, 515 : 266 - 271
  • [10] Central Discontinuous Galerkin Method for the Navier-Stokes Equations
    Ren, Tan (rentanx@126.com), 2017, Beijing Institute of Technology (26):
12345