Anisotropic Hybrid Weakly Over-Penalized Symmetric Interior Penalty Method for Poisson Equation

The author proposes a new hybrid-type anisotropic weakly over-penalized symmetric interior penalty (HWOPSIP) method for solving the Poisson equation on convex domains. The key idea is to apply the relation between the Raviart-Thomas finite element space and a discontinuous space, which allows for optimal error estimates of the consistency error on anisotropic meshes.