A hybridized formulatibn for the weak Galerkin mixed finite element method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:307

Article; Proceedings Paper

Mu, Lin¹  Wang, Junping²  Ye, Xiu³ 

[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

关键词: Weak Galerkin;    Finite element methods;    Discrete weak divergence;    Second-order elliptic problems;    Hybridized mixed finite element methods;   

DOI  :  10.1016/j.cam.2016.01.004

来源: Elsevier

【 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.

【 授权许可】

Free