A hybridized formulatibn for the weak Galerkin mixed finite element method

被引:22
|
作者
Mu, Lin [1 ]
Wang, Junping [2 ]
Ye, Xiu [3 ]
机构
[1] Oak Ridge Natl Lab, Comp Sci & Math Div, Oak Ridge, TN 37831 USA
[2] Natl Sci Fdn, Div Math Sci, 4201 Wilson Blvd, Arlington, VA 22230 USA
[3] Univ Arkansas, Dept Math, Little Rock, AR 72204 USA
基金
美国国家科学基金会;
关键词
Weak Galerkin; Finite element methods; Discrete weak divergence; Second-order elliptic problems; Hybridized mixed finite element methods; ELLIPTIC PROBLEMS;
D O I
10.1016/j.cam.2016.01.004
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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. (C) 2016 Elsevier B.V. All rights reserved.
引用
收藏
页码:335 / 345
页数:11
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