A Linearized Stabilizer Free Weak Galerkin Method and its Optimal L2 Error Estimations for the High-Field Model (pp.107-138)

This paper concerns a linearized stabilizer-free weak Galerkin finite element method (SFWGFEM) for the two-dimensional high-field (HF) model.The proposed method not only offers the flexibility to approximate functions and is compatible with meshes including hanging nodes as WG-FEM, but also maintains a simple format similar to the traditional finite element method.Optimal error estimations are obtained in both L 2 and energy norms through the introduction of a weak Galerkin Ritz projection operator, where the associated Ritz projection error is derived by a dual problem.The superconvergent results between the Ritz projection of the exact function and the numerical solution in the energy norm lead to optimal L 2 estimations.Numerical experiments are conducted to demonstrate the theoretical analysis.