Question

What is the number of nodes present on the boundary of the Lagrange quadratic rectangular element used in FEM?

(a) 1

(b) 4

(c) 8

(d) 9

The question was asked in quiz.

This intriguing question originated from Library of Elements and Interpolation Functions in section Interpolation Functions, Numerical Integration and Modelling Considerations of Finite Element Method

Answer 1

The correct choice is (c) 8

Explanation: The Lagrange quadratic rectangular element has nine regularly spaced nodes. Four nodes are paced at the four corners, four at midpoints of the sides, and one at the center of the element. Thus, a total of 8 boundary nodes are present. Its associated polynomial has a total of nine terms, including the second degree and third-degree terms.