Quasi-optimal nonconforming methods for symmetric elliptic problems. III -- DG and other interior penalty methods
Abstract
We devise new variants of the following nonconforming finite element methods: DG methods of fixed arbitrary order for the Poisson problem, the Crouzeix-Raviart interior penalty method for linear elasticity, and the quadratic interior penalty method for the biharmonic problem. Each variant differs from the original method only in the discretization of the right-hand side. Before applying the load functional, a linear operator transforms nonconforming discrete test functions into conforming functions such that stability and consistency are improved. The new variants are thus quasi-optimal with respect to an extension of the energy norm. Furthermore, their quasi-optimality constants are uniformly bounded for shape regular meshes and tend to as the penalty parameter increases.
Keywords
Cite
@article{arxiv.1710.03452,
title = {Quasi-optimal nonconforming methods for symmetric elliptic problems. III -- DG and other interior penalty methods},
author = {Andreas Veeser and Pietro Zanotti},
journal= {arXiv preprint arXiv:1710.03452},
year = {2017}
}