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.
- Research Organization:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- ERKJE45; AC05-00OR22725
- OSTI ID:
- 1769965
- Alternate ID(s):
- OSTI ID: 1323958; OSTI ID: 1338538
- Journal Information:
- Journal of Computational and Applied Mathematics, Journal Name: Journal of Computational and Applied Mathematics Vol. 307 Journal Issue: C; ISSN 0377-0427
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- Belgium
- Language:
- English
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