Polynomials are generally used as shape function due to the following reasons. ... The accuracy of the results can be improved by increasing the order of the polynomial. 3. It is easy to formulate and computerize the finite element equations.

Why do we use shape function?

We need to derive a function to compute values of the temperature at locations between the nodes. This interpolation function is called the shape function. We demonstrate its derivation for a 1-dimensional linear element here. Note that, for linear elements, the polynomial inerpolation function is first order.

Why are polynomials often used in interpolation?

If a set of data contains n known points, then there exists exactly one polynomial of degree n-1 or smaller that passes through all of those points. ... This methodology, known as polynomial interpolation, often (but not always) provides more accurate results than linear interpolation.