LBB Stability of a Mixed Discontinuous/Continuous Galerkin Finite Element Pair
Abstract
We introduce a new mixed discontinuous/continuous Galerkin finite element for solving the 2- and 3-dimensional wave equations and equations of incompressible flow. The element, which we refer to as P1dg-P2, uses discontinuous piecewise linear functions for velocity and continuous piecewise quadratic functions for pressure. The aim of introducing the mixed formulation is to produce a new flexible element choice for triangular and tetrahedral meshes which satisfies the LBB stability condition and hence has no spurious zero-energy modes. We illustrate this property with numerical integrations of the wave equation in two dimensions, an analysis of the resultant discrete Laplace operator in two and three dimensions, and a normal mode analysis of the semi-discrete wave equation in one dimension.
Keywords
Cite
@article{arxiv.0707.4607,
title = {LBB Stability of a Mixed Discontinuous/Continuous Galerkin Finite Element Pair},
author = {C. J. Cotter and D. A. Ham and C. C. Pain and S. Reich},
journal= {arXiv preprint arXiv:0707.4607},
year = {2007}
}