Shape Function and Their Evaluation
Let us focus on evaluation of 
Now, we can express  and  as
The interpolation function  and  can be thought of as influence function which determine the influence of the corresponding node  or  at an interior point  of the element. An alternate name for these interpolation functions is shape functions and they have the following properties:
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And has some magnitude between 0 and 1 for intermediate point. Similarly,
As such, Eq 19.11 can be written as  within each element. From now on, we shall use the notation  and  to denote these shape functions, where the number 1,2,3 stand for local numbers of the nodes assigned with respect to the element under consideration.
This gives
During the global solution of all the nodal temperatures, the nodes may be given any global number (with respect to the whole domain). The correspondence between the local and the global node numbers are usually stored in the arrays. Such arrays are called element connectivity in most of the FEM codes.
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