🚀 go-pugleaf

In article <1992Dec15.092610@roper.mc.ti.com> W. Donald Rolph:
> You are indeed confused.

I am never confused about these things.

>  Any approximation procedure must have trial functions.

No, no.

> In traditional FEA they are called shape functions, choose the name you like
> but all FEA procedures must have some approximating function over the domain
> space.

*All* procedures?

Gee, how then could I calculate the temperature distribution in a sodium pump
by an direct FE method, WITHOUT ever needing such "approximating functions"?
(An accompanying article is called "Multimode Heat Transfer in Sodium Pumps".
It is found in the Proceedings of the 0Xth Conference on Numerical Methods
in Thermal, or whatever, Problems, Swansea U.K., 197X. Look it up ;-)

I also did some work on pure advection without shape functions. But who am I?
There exists CFD code named "FLOTRAN", which has a "streamline upwind" scheme
in it, derived directly without shape functions. It's all in my SUNA articles.

And almost any Finite Element book starts with the assembly of resistor-like
elements, without approximations. The element-matrix of an electrical resistor
is derived directly by applying the laws of Ohm and Kirchhoff, giving:

         | +1/R  -1/R |
         | -1/R  +1/R |

Just define the connectivity (no coordinates) of your resistor-network,
two voltages as a boundary condition, and go ...
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