Core Concepts
The author proposes an anisotropic weakly over-penalized symmetric interior penalty (WOPSIP) method for solving the Stokes 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 an optimal error estimate of the consistency error on anisotropic meshes.
Abstract
The author investigates an anisotropic WOPSIP method for the Stokes equation on convex domains. The WOPSIP method is a simple discontinuous Galerkin method similar to the Crouzeix-Raviart finite element method.
The main contributions are:
The author shows a new proof for the consistency term, which allows for an estimate of the anisotropic consistency error. The key idea is to apply the relation between the Raviart-Thomas finite element space and a discontinuous space.
The author shows that the Stokes element satisfies the inf-sup condition on anisotropic meshes, even though inf-sup stable schemes of the discontinuous Galerkin method on shape-regular mesh partitions have been widely discussed.
The author provides an error estimate in an energy norm on anisotropic meshes.
In the numerical experiments, the author compares calculation results for standard and anisotropic mesh partitions.