Further studies on equalorder interpolation for NavierStokes
Abstract
The simplest quadrilateral element available for the incompressible NavierStokes equations is the mixed interpolation 4node element with bilinear velocity and (piecewise) constant pressure  donoted herein by 4/1. The next simplest is the 4/4 element, in which (continuous) bilinear approximation is also employed for pressure  i.e., the simplest case of equalorder interpolation. The 4/1 element has been very popular, even though it sometimes generates one spurious pressure mode which is usually filterable. But the 4/1 element generates a poor approximation to (Del P) when distorted elements are employed (via the bilinear isoparamatic technique), which often leads to large errors in velocity; e.g. this element generated wrong answers for vortex shedding on the same mesh for which a higher order element (9/4:) performed well. Although the 4/4 element generates ostensibly useless pressures, the pressure gradient and the velocity field might be much more accurate than those from the 4/1 element, especially when distorted meshes are employed. Based on these observations, the 4/4 element was tested on two problems, for which the 4/1 element failed. The 4/4 element is no panacea, however; the multiple (and generally unknown) spurious pressure modes (pure and impure) associated with equalorder interpolation leads to a generally delicate solution procedure. A viable technique for recovering a useful pressure field from the otherwise polluted pressures is presented.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 October 1983
 Bibcode:
 1983STIN...8413512G
 Keywords:

 Finite Element Method;
 Interpolation;
 NavierStokes Equation;
 Pressure Gradients;
 Velocity Distribution;
 Vortices;
 Approximation;
 Incompressibility;
 Fluid Mechanics and Heat Transfer