A hybridized formulatibn for the weak Galerkin mixed finite element method

作者：Mu Lin; Wang Junping; Ye Xiu^*

来源：Journal of Computational and Applied Mathematics, 2016, 307: 335-345.

DOI：10.1016/j.cam.2016.01.004

• Weak Galerkin
• Finite element methods
• Discrete weak divergence
• Second-order elliptic problems
• Hybridized mixed finite element methods

This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising from the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. Some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.

• 出版日期2016-12-1
• 单位国家自然科学基金委员会