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Title: A hybridized formulation for the weak Galerkin mixed finite element method

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. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.
Authors:
 [1] ;  [2] ; ORCiD logo [3]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
  2. National Science Foundation, Arlington, VA (United States). Division of Mathematical Sciences
  3. University of Arkansas at Little Rock (Arkansas). Department of Mathematics
Publication Date:
OSTI Identifier:
1338538
Grant/Contract Number:
AC05-00OR22725; ERKJE45
Type:
Accepted Manuscript
Journal Name:
Journal of Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 307; Journal Issue: C; Journal ID: ISSN 0377-0427
Publisher:
Elsevier
Research Org:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Weak Galerkin; Finite element methods; Discrete weak divergence; Second-order elliptic problems; Hybridized mixed finite element methods