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

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

2007-07-31

arxiv.org/abs/0707.4607v1

Mathematics

Numerical Analysis

Scientific paper

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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