Analysis of Some LowOrder Finite Element Schemes for the NavierStokes Equations
Abstract
Various loworder finite element schemes for the NavierStokes equations are analysed, including the commonly used bilinear velocity, piecewise constant pressure element, and the algorithms based on the finite element analogue of the MAC stencil discussed in a companion paper. By performing a truncation error analysis using a variety of different assumptions about how the nodal parameters represent the data, it is shown how a more complete picture of the behaviour of the algorithms can be obtained. In particular, differences in performance on coarse grids using algorithms which have the same asymptotic convergence rate can be explained.
 Publication:

Journal of Computational Physics
 Pub Date:
 August 1983
 DOI:
 10.1016/00219991(83)900931
 Bibcode:
 1983JCoPh..51..273C
 Keywords:

 Computational Fluid Dynamics;
 Error Analysis;
 Finite Element Method;
 NavierStokes Equation;
 Truncation Errors;
 Advection;
 Algorithms;
 Asymptotic Methods;
 Computational Grids;
 Convergence;
 Diffusion Theory;
 Numerical Stability;
 Fluid Mechanics and Heat Transfer