| [1] Arnold D, Brezzi F, Cockburn B and Marini D. Unified analysis of discontinuous Galerkin methods for elliptic problems[J]. SIAM Journal on Numerical Analysis, 2002, 39:1749-1779.[2] Bassi F and Rebay S. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations[J]. Journal of Computational Physics, 1997, 131:267-279.[3] Chen L, Wang J, Wang Y and Ye X. An Auxiliary Space Multigrid Preconditioner for the Weak Galerkin Method[J]. Computers and Mathematics with Applications, 2015, 70:330-344.[4] Chen L,Wang J and Ye X. A posteriori error estimates for Weak Galerkin finite element methods for second order elliptic problem[J]. Journal of Scientific Computing, 2014, 59:496-511.[5] Chen W, Wang F and Wang Y. Weak Galerkin method for the coupled Darcy-Stokes flow, IMA Journal of Numerical Analysis, DOI:10.1093/imanum/drv0121.70.[6] Cockburn B and Cui J. An analysis of HDG methods for the vorticity-velocity-pressure formulation of the Stokes problem in three dimensions[J]. Mathematics of Computation, 2012, 81:1355-1368.[7] Cockburn B, Gopalakrishnan J and Lazarov R. Unified hybridization of discontinuous Galerkin, mixed, and conforming Galerkin methods for second order elliptic problems[J]. SIAM Journal on Numerical Analysis, 2009, 47:1319-136.[8] Cockburn B and Shu C W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems[J]. SIAM Journal on Numerical Analysis, 1998, 35:2440-2463.[9] Harris A and Harris S. Superconvergence of weak Galerkin finite element approximation for second order elliptic problems by L2 projections[J]. Journal of Applied Mathematics and Computation, 2014, 227:610-621.[10] HuangW and Wang Y. Anisotropic mesh quality measures and adaptation for polygonal meshes. arXiv:1507.08243[11] Li Binjie and Xie Xiaoping. Multigrid weak Galerkin finite element method for diffusion problems. arXiv:1405.7506[12] Li Q and Wang J. Weak Galerkin Finite Element Methods for Parabolic Equations, Numerical Methods for Partial Differential Equations, DOI:10.1002/num.21786. arXiv:1212.3637[13] Mu L, Wang J, Wang Y and Ye X. A weak Galerkin mixed finite element method for biharmonic equations[J]. Numerical Solution of Partial Differential Equations:Theory, Algorithms, and Their Applications, 2013, 45:247-277.[14] Mu L, Wang J, Ye X, Zhang S. C0 Weak Galerkin finite element methods for the biharmonic equation[J]. Journal of Scientific Computing, 2014, 59:437-495.[15] Mu L, Wang J and Ye X. A weak Galerkin finite element method for biharmonic equations on polytopal meshes[J]. Numerical Methods for Partial Differential Equations, 2014, 30:1003-1029.[16] Mu L, Wang J, Ye X and Zhao S. Numerical studies on the Weak Galerkin method for the Helmholtz equation with large wave number[J]. Communications in Computational Physics, 2014, 15:1461-1479.[17] Mu L, Wang J and Ye X. Weak Galerkin finite element method for the Helmholtz equation with large wave number on polytopal meshes, IMA, doi:10.1093/imanum/dru026.[18] Mu L, Wang J and Ye X. A stable numerical algorithm for the Brinkman equations by weak Galerkin finite element methods[J]. Journal of Computational Physics, 2014, 273:327-342.[19] Mu L, Wang J and Ye X,Weak Galerkin finite element method for second-order elliptic problems on polytopal meshes[J]. International Journal of Numerical Analysis and Modeling, 2015, 12:31-53.[20] Mu L, Wang J, and Ye X. A weak Galerkin finite element method with polynomial reduction[J]. Journal of Computational and Applied Mathematics, 2015, 285:45-58.[21] Mu L, Wang J, Wei G, Ye X and Zhao S. Weak Galerkin method for the elliptic interface problem[J]. Journal of Computational Physics, 2013, 250:106-125.[22] Mu L, Wang J, Ye X and Zhang S. A weak Galerkin finite element method for the Maxwell equations[J]. Journal of Scientific Computing, 2015, 65:363-386.[23] Raviart P and Thomas J. A mixed finite element method for second order elliptic problems, Mathematical Aspects of the Finite Element Method, I. Galligani, E. Magenes, eds., Lectures Notes in Math. 606, Springer-Verlag, New York, 1977.[24] Wang C andWang J. An efficient numerical scheme for the biharmonic equation by weak Galerkin finite element methods on polygonal or polyhedral meshes[J]. Journal of Computers and Mathematics with Applications, 2014, 68:2314-2330.[25] Wang C and Wang J. Discretization of div-curl systems by weak Galerkin finite element methods on polyhedral partitions. arXiv:1501.04616[26] Wang C, Wang J, Wang R and Zhang R. A Locking-Free Weak Galerkin Finite Element Method for Elasticity Problems in the Primal Formulation[J]. Journal of Computational and Applied Mathematics, to appear. arXiv:1508.03855v1[27] Wang J and Wang C. Weak Galerkin finite element methods for elliptic PDEs (in Chinese)[J]. Sci Sin Math, 2015, 45:1061-1092, doi:10.1360/N012014-00233.[28] Wang J and Ye X. A weak Galerkin finite element method for second order elliptic problems[J]. Journal of Computational and Applied Mathematics, 2013, 241:103-115. arXiv:1104.2897v1[29] Wang J and Ye X. A Weak Galerkin mixed finite element method for second-order elliptic problems[J]. Mathematics of Computation, 2014, 83:2101-2126. arXiv:1202.3655v1[30] Wang J and Ye X. A weak Galerkin finite element method for the Stokes equations, Advances in Computational Mathematics, May, 2015. DOI 10.1007/s10444-015-9415-2. arXiv:1302.2707v1[31] Wang R, Wang X, Zhai Q and Zhang R. A Weak Galerkin Finite Element Scheme for solving the stationary Stokes Equations[J]. Journal of Computational and Applied Mathematics, to appear.[32] Yan J and Shu C W. A local discontinuous Galerkin method for KdV type equations[J]. SIAM Journal on Numerical Analysis, 2002, 40:769-791.[33] Zhai Q, Zhang R and Wang X. A Hybridized Weak Galerkin Finite Element Scheme for the Stokes Equations[J]. Sci China Math, 2015, 58:2455-2472.[34] Zhang R and Zhai Q. A weak Galerkin finite element scheme for the biharmonic equations by using polynomials of reduced order[J]. Journal of Scientific Computing, 2015, 64:559-585. |
