### Electronic Research Archive

2020, Issue 2: 821-836. doi: 10.3934/era.2020042
Special Issues

# A hybridized weak Galerkin finite element scheme for general second-order elliptic problems

• Received: 01 February 2020 Revised: 01 March 2020
• Primary: 65N15, 65N30; Secondary: 35J50

• In this paper, a hybridized weak Galerkin (HWG) finite element scheme is presented for solving the general second-order elliptic problems. The HWG finite element scheme is based on the use of a Lagrange multiplier defined on the element boundaries. The Lagrange multiplier provides a numerical approximation for certain derivatives of the exact solution. It is worth pointing out that a skew symmetric form has been used for handling the convection term to get the stability in the HWG formulation. Optimal order error estimates are derived for the corresponding HWG finite element approximations. A Schur complement formulation of the HWG method is introduced for implementation purpose.

Citation: Guanrong Li, Yanping Chen, Yunqing Huang. A hybridized weak Galerkin finite element scheme for general second-order elliptic problems[J]. Electronic Research Archive, 2020, 28(2): 821-836. doi: 10.3934/era.2020042

### Related Papers:

• In this paper, a hybridized weak Galerkin (HWG) finite element scheme is presented for solving the general second-order elliptic problems. The HWG finite element scheme is based on the use of a Lagrange multiplier defined on the element boundaries. The Lagrange multiplier provides a numerical approximation for certain derivatives of the exact solution. It is worth pointing out that a skew symmetric form has been used for handling the convection term to get the stability in the HWG formulation. Optimal order error estimates are derived for the corresponding HWG finite element approximations. A Schur complement formulation of the HWG method is introduced for implementation purpose.

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