# Representation of polynomial order in CFD codes

I am currently working on a CFD code over a cubic grid. Now, the number of elements used in the simulation is decomposed among the number of processors. Each of those processors (a section of the cube) is then divided up in a number of elements that corresponds to the polynomial order. I would like to understand the mathematical reason of doing so. • What's your question? – Bill Barth May 19 '15 at 12:04
• @BillBarth My question is why elements are also divided in the number of polynomial order. How is that related – Manolete May 19 '15 at 12:48
• Elements aren't subdivided. They require some sort of non-corner points or degrees of freedom to represent the polynomial functions they represent, but they're not really "divided". – Bill Barth May 19 '15 at 14:53

## 1 Answer

What you have is most likely a mesh for a Spectral Element Method or something similar). The solution is represented using a high order polynomial each section of the cube (referred to as an element). For convenience, these polynomials are represented as Lagrange nodal functions, which are associated with a set of points on each element (which are denoted by the vertices of the sub-mesh on each cube).

High order methods tend to be more accurate than a low order method, at least when measured in terms of error as a function of the element size, and are fairly simple to make efficient on modern hardwares.