A weak Galerkin finite element method for the Navier-Stokes equations

[1]  J. Tinsley Oden,et al.  Analysis of Flow of Viscous Fluids by the Finite-Element Method , 1972 .

[2]  I. Babuska,et al.  Nonconforming Elements in the Finite Element Method with Penalty , 1973 .

[3]  P. Raviart,et al.  Conforming and nonconforming finite element methods for solving the stationary Stokes equations I , 1973 .

[4]  P. Hood,et al.  A numerical solution of the Navier-Stokes equations using the finite element technique , 1973 .

[5]  F. Brezzi.  On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers , 1974 .

[6]  R. Temam,et al.  Navier-Stokes equations: theory and numerical analysis: R. Teman North-Holland, Amsterdam and New York. 1977. 454 pp. US $45.00 , 1978 .

[7]  M. Fortin,et al.  A non‐conforming piecewise quadratic finite element on triangles , 1983 .

[8]  Vivette Girault,et al.  Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms , 1986, Springer Series in Computational Mathematics.

[9]  M. Crouzeix,et al.  Nonconforming finite elements for the Stokes problem , 1989 .

[10]  Chi-Wang Shu,et al.  The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V , 1998 .

[11]  S. Rebay,et al.  A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations , 1997 .

[12]  George Em Karniadakis,et al.  A discontinuous Galerkin method for the Navier-Stokes equations , 1999 .

[13]  George Em Karniadakis,et al.  The Development of Discontinuous Galerkin Methods , 2000 .

[14]  Douglas N. Arnold,et al.  Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems , 2001, SIAM J. Numer. Anal..

[15]  Gene H. Golub,et al.  Numerical solution of saddle point problems , 2005, Acta Numerica.

[16]  Jaap J. W. van der Vegt,et al.  Space-Time Discontinuous Galerkin Method for the Compressible Navier-Stokes , 2006 .

[17]  Guido Kanschat,et al.  A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier–Stokes Equations , 2007, J. Sci. Comput..

[18]  Ye,et al.  FINITE ELEMENT METHODS FOR THE NAVIER-STOKES EQUATIONS BY H(div)ELEMENTS , 2008 .

[19]  Jaime Peraire,et al.  Discontinuous Galerkin Solution of the Navier-Stokes Equations on Deformable Domains , 2007 .

[20]  Bernardo Cockburn,et al.  An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations , 2011, J. Comput. Phys..

[21]  Junping Wang,et al.  A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation with Large Wave Numbers , 2011, 1310.6005.

[22]  Junping Wang,et al.  Weak Galerkin finite element methods for Parabolic equations , 2012, 1212.3637.

[23]  Junping Wang,et al.  A computational study of the weak Galerkin method for second-order elliptic equations , 2011, Numerical Algorithms.

[24]  Junping Wang,et al.  Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes , 2013, 1303.0927.

[25]  F. Brezzi,et al.  Basic principles of Virtual Element Methods , 2013 .

[26]  M. Fortin,et al.  Mixed Finite Element Methods and Applications , 2013 .

[27]  Junping Wang,et al.  A weak Galerkin finite element method for second-order elliptic problems , 2011, J. Comput. Appl. Math..

[28]  Shan Zhao,et al.  WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS. , 2013, Journal of computational physics.

[29]  Fuzheng Gao,et al.  A modified weak Galerkin finite element method for a class of parabolic problems , 2014, J. Comput. Appl. Math..

[30]  Junping Wang,et al.  A weak Galerkin mixed finite element method for second order elliptic problems , 2012, Math. Comput..

[31]  Guang Lin,et al.  Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity , 2014, J. Comput. Phys..

[32]  Lin Mu,et al.  A stable numerical algorithm for the Brinkman equations by weak Galerkin finite element methods , 2013, J. Comput. Phys..

[33]  Junping Wang,et al.  An efficient numerical scheme for the biharmonic equation by weak Galerkin finite element methods on polygonal or polyhedral meshes , 2013, Comput. Math. Appl..

[34]  Lin,et al.  ON L2 ERROR ESTIMATE FOR WEAK GALERKIN FINITE ELEMENT METHODS FOR PARABOLIC PROBLEMS , 2014 .

[35]  Chunmei Wang,et al.  A Hybridized Weak Galerkin Finite Element Method for the Biharmonic Equation , 2014 .

[36]  Wenbin Chen,et al.  Weak Galerkin method for the coupled Darcy-Stokes flow , 2014, 1407.5604.

[37]  Lin Mu,et al.  A modified weak Galerkin finite element method for the Stokes equations , 2015, J. Comput. Appl. Math..

[38]  Junping Wang,et al.  A weak Galerkin finite element method with polynomial reduction , 2013, J. Comput. Appl. Math..

[39]  Alexandre Ern,et al.  Hybrid high-order methods for variable-diffusion problems on general meshes , 2015 .

[40]  Weifeng Qiu,et al.  A superconvergent HDG method for the Incompressible Navier-Stokes Equations on general polyhedral meshes , 2015, 1506.07543.

[41]  Alexandre Ern,et al.  A Discontinuous-Skeletal Method for Advection-Diffusion-Reaction on General Meshes , 2015, SIAM J. Numer. Anal..

[42]  Lin Mu,et al.  A new weak Galerkin finite element method for the Helmholtz equation , 2015 .

[43]  Junping Wang,et al.  A weak Galerkin finite element method for the stokes equations , 2013, Adv. Comput. Math..

[44]  Xin Liu,et al.  A weak Galerkin finite element method for the Oseen equations , 2016, Adv. Comput. Math..

[45]  Alessandro Russo,et al.  Mixed Virtual Element Methods for general second order elliptic problems on polygonal meshes , 2014, 1506.07328.

[46]  Ruishu Wang,et al.  A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation , 2015, J. Comput. Appl. Math..

[47]  Ye Xiu.  A WEAK GALERKIN METHOD FOR THE REISSNER-MINDLIN PLATE IN PRIMARY FORM , 2017 .

[48]  Xiaozhe Hu,et al.  Weak Galerkin method for the Biot's consolidation model , 2017, Comput. Math. Appl..

[49]  Hengguang Li,et al.  A Posteriori Error Estimates for the Weak Galerkin Finite Element Methods on Polytopal Meshes , 2019, Communications in Computational Physics.