In this paper, a combined hybrid method is applied to finite element discretization of plate bending problems. It is shown that the resultant schemes are stabilized, i.e., the convergence of the schemes is independent...In this paper, a combined hybrid method is applied to finite element discretization of plate bending problems. It is shown that the resultant schemes are stabilized, i.e., the convergence of the schemes is independent of inf-sup conditions and any other patch test. Based on this, two new series of plate elements are proposed.展开更多
This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress...This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.展开更多
Based on combination of two variational principles, a nonconforming stabilized finite element method is presented for the Reissner-Mindlin plates. The method is convergent when the finite element space is energy-compa...Based on combination of two variational principles, a nonconforming stabilized finite element method is presented for the Reissner-Mindlin plates. The method is convergent when the finite element space is energy-compatible. Error estimates are derived. In particular, three finite element spaces are applied in the computation. Numerical results show that the method is insensitive to the mesh distortion and has better performence than the MITC4 and DKQ methods. With properly chosen parameters, high accuracy can be obtained at coarse meshes.展开更多
In this paper a hybridized weak Galerkin(HWG) finite element method for solving the Stokes equations in the primary velocity-pressure formulation is introduced.The WG method uses weak functions and their weak derivati...In this paper a hybridized weak Galerkin(HWG) finite element method for solving the Stokes equations in the primary velocity-pressure formulation is introduced.The WG method uses weak functions and their weak derivatives which are defined as distributions.Weak functions and weak derivatives can be approximated by piecewise polynomials with various degrees.Different combination of polynomial spaces leads to different WG finite element methods,which makes WG methods highly flexible and efficient in practical computation.A Lagrange multiplier is introduced to provide a numerical approximation for certain derivatives of the exact solution.With this new feature,the HWG method can be used to deal with jumps of the functions and their flux easily.Optimal order error estimates are established for the corresponding HWG finite element approximations for both primal variables and the Lagrange multiplier.A Schur complement formulation of the HWG method is derived for implementation purpose.The validity of the theoretical results is demonstrated in numerical tests.展开更多
A hybridization technique is applied to the weak Galerkin finite element method （WGFEM） for solving the linear elasticity problem in mixed form. An auxiliary function, the Lagrange multiplier defined on the boundary...A hybridization technique is applied to the weak Galerkin finite element method （WGFEM） for solving the linear elasticity problem in mixed form. An auxiliary function, the Lagrange multiplier defined on the boundary of elements, is introduced in this method. Consequently, the computational costs are much lower than the standard WGFEM. Optimal order error estimates are presented for the approximation scheme. Numerical results are provided to verify the theoretical results.展开更多
基金This work was supported by the National Science Foundation of China
文摘In this paper, a combined hybrid method is applied to finite element discretization of plate bending problems. It is shown that the resultant schemes are stabilized, i.e., the convergence of the schemes is independent of inf-sup conditions and any other patch test. Based on this, two new series of plate elements are proposed.
文摘This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.
基金supported by the Key Technologies R&D Program of Sichuan Province of China(No. 05GG006-006-2)
文摘Based on combination of two variational principles, a nonconforming stabilized finite element method is presented for the Reissner-Mindlin plates. The method is convergent when the finite element space is energy-compatible. Error estimates are derived. In particular, three finite element spaces are applied in the computation. Numerical results show that the method is insensitive to the mesh distortion and has better performence than the MITC4 and DKQ methods. With properly chosen parameters, high accuracy can be obtained at coarse meshes.
基金supported by National Natural Science Foundation of China(Grant Nos.11271157,11371171 and 11471141)the Program for New Century Excellent Talents in University of Ministry of Education of China
文摘In this paper a hybridized weak Galerkin(HWG) finite element method for solving the Stokes equations in the primary velocity-pressure formulation is introduced.The WG method uses weak functions and their weak derivatives which are defined as distributions.Weak functions and weak derivatives can be approximated by piecewise polynomials with various degrees.Different combination of polynomial spaces leads to different WG finite element methods,which makes WG methods highly flexible and efficient in practical computation.A Lagrange multiplier is introduced to provide a numerical approximation for certain derivatives of the exact solution.With this new feature,the HWG method can be used to deal with jumps of the functions and their flux easily.Optimal order error estimates are established for the corresponding HWG finite element approximations for both primal variables and the Lagrange multiplier.A Schur complement formulation of the HWG method is derived for implementation purpose.The validity of the theoretical results is demonstrated in numerical tests.
文摘A hybridization technique is applied to the weak Galerkin finite element method （WGFEM） for solving the linear elasticity problem in mixed form. An auxiliary function, the Lagrange multiplier defined on the boundary of elements, is introduced in this method. Consequently, the computational costs are much lower than the standard WGFEM. Optimal order error estimates are presented for the approximation scheme. Numerical results are provided to verify the theoretical results.
