论文信息 - A modified weak Galerkin finite element method for the Stokes equations

A modified weak Galerkin finite element method for the Stokes equations

A modified weak Galerkin (MWG) finite element method is introduced for the Stokes equations in the primary velocity-pressure formulation. This method is based on the weak Galerkin (WG) finite element method developed recently in Wang and Ye (0000). The unknowns associated with element boundaries in the WG method have been eliminated in the MWG method. As the result, the MWG method has fewer degrees of freedom. Optimal-order error estimates are established for the corresponding numerical approximation in various norms. Numerical results are presented to confirm the theory.

[1] L. R. Scott,et al. The Mathematical Theory of Finite Element Methods , 1994 .

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

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

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

[5] Michel Fortin,et al. Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

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

[7] I. Babuska. The finite element method with Lagrangian multipliers , 1973 .

[8] John A. Trangenstein,et al. Mixed and Hybrid Finite Elements , 2013 .

[9] Max Gunzburger,et al. Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice, and Algorithms , 1989 .