LBB Stability of a Mixed Discontinuous/Continuous Galerkin Finite Element Pair
نویسندگان
چکیده
We introduce a new mixed discontinuous/continuous Galerkin finite element for solving the 2and 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.
منابع مشابه
LBB stability of a mixed Galerkin finite element pair for fluid flow simulations
We introduce a new mixed finite element for solving the 2and 3-dimensional wave equations and equations of incompressible flow. The element, which we refer to as P1D-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 t...
متن کاملA note on accurate and efficient higher order Galerkin time stepping schemes for the nonstationary Stokes equations
In this note, we extend our recent work for the heat equation in [1] and compare numerically continuous Galerkin-Petrov (cGP) and discontinuous Galerkin (dG) time discretizations for the nonstationary Stokes equations in two dimensions. For the space discretization, we use the LBB-stable finite element pair Q2/P disc 1 and we discuss implementation aspects as well as methods for solving the res...
متن کاملNon-Linear Petrov-Galerkin Methods for Reduced Order Modelling of the Nav‐ ier-Stokes Equations using a Mixed Finite Element Pair
A new nonlinear Petrov-Galerkin approach has been developed for Proper Orthogonal Decomposition (POD) Reduced Order Modelling (ROM) of the Navier-Stokes equations. The new method is based on the use of the cosine rule between the advection direction in Cartesian space-time and the direction of the gradient of the solution. A finite element pair, P1DGP2, which has good balance preserving propert...
متن کاملConvergence of a Discontinuous Galerkin Method for the Miscible Displacement under Minimal Regularity
Discontinuous Galerkin time discretizations are combined with the mixed finite element and continuous finite element methods to solve the miscible displacement problem. Stable schemes of arbitrary order in space and time are obtained. Under minimal regularity assumptions on the data, convergence of the scheme is proved by using compactness results for functions that may be discontinuous in time.
متن کاملImplementation of the Continuous-Discontinuous Galerkin Finite Element Method
For the stationary advection-diffusion problem the standard continuous Galerkin method is unstable without some additional control on the mesh or method. The interior penalty discontinuous Galerkin method is stable but at the expense of an increased number of degrees of freedom. The hybrid method proposed in [5] combines the computational complexity of the continuous method with the stability o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008