[Nek5000-users] Basis functions and smoothness of interpolants

[nek5000-users at lists.mcs.anl.gov]

Hi,


I am trying to understand how the code works, and therefore I opened the theory section at the Nek5000-homepage.

Here, you link to the book "High-Order Methods for Incompressible Fluid Flow" by Deville et al.

I started to read the book, but I am not sure how to relate what I read to Nek.


In chapter 4, a class of 2D basis functions defined on a square is defined.

I think this is the kind of basis function that is used in Nek, am I right?


I understand that these functions serves as a basis for one element of the domain.

But Nek solves PDE:s over several linked elements.

What is here the condition at the edge connecting two elements?


Is it that the function (velocity component/pressure/scalar) should be continuous at the GLL-nodes at such an edge?

Also consinuously differentiable att these nodes? Differentiable to some higher order?

What about function values on the edge that are not at the GLL-node?

Are they discontinuous or differentiable to some certain order?


Best,


Johan



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