Higher Polynomial Order Basis Functions — Lesson 2

In this lesson, the basis functions will be developed from one dimension to a higher-order polynomial basis function. After developing a higher-order polynomial basis function for Lagrange polynomials, the general formula for an arbitrary order polynomial is written. The discussion starts with the quadratic basis function and is continued further.

 

Correction to Board work

 

The video starts with a discussion on some points about the Lagrange polynomials used in the previous video. After discussing the above points, finite element (FE) formulation is developed with a quadratic basis function.

 

The development of FE formulation is continued, and the invertibility of the map and Isoparametric mapping is discussed and used at the start. It is shown that the gradients can be calculated easily which are finally used in evaluating the integrals. It is shown that the tangent of the geometric mapping is constant. Affine mapping is defined.

 

The discussion continues from the previous lesson on the evaluation of integral. The integral is written in even simpler forms using some of the properties of Lagrange polynomials. In the end, the results are written collectively, and the element stiffness matrix is shown.