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arXiv · 0707.4607

LBB Stability of a Mixed Discontinuous/Continuous Galerkin Finite Element Pair

C. J. Cotter·D. A. Ham·C. C. Pain·S. Reich
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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.

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C. J. Cotter, D. A. Ham, C. C. Pain, S. Reich. 2007-07-31. LBB Stability of a Mixed Discontinuous/Continuous Galerkin Finite Element Pair. https://arxiv.org/abs/0707.4607

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