English

Stable discontinuous Galerkin FEM without penalty parameters

Numerical Analysis 2017-02-17 v2

Abstract

We propose a modified local discontinuous Galerkin (LDG) method for second--order elliptic problems that does not require extrinsic penalization to ensure stability. Stability is instead achieved by showing a discrete Poincar\'e--Friedrichs inequality for the discrete gradient that employs a lifting of the jumps with one polynomial degree higher than the scalar approximation space. Our analysis covers rather general simplicial meshes with the possibility of hanging nodes.

Keywords

Cite

@article{arxiv.1602.04625,
  title  = {Stable discontinuous Galerkin FEM without penalty parameters},
  author = {Lorenz John and Michael Neilan and Iain Smears},
  journal= {arXiv preprint arXiv:1602.04625},
  year   = {2017}
}

Comments

Accepted for publication in the conference proceedings of Numerical Mathematics and Advanced Applications ENUMATH 2015. Typo corrected

R2 v1 2026-06-22T12:50:16.211Z