Question

In FEM, which option is not correct about the Lagrange family of triangular elements?

(a) The nodes are uniformly spaced

(b) Pascal’s triangle can be viewed as a triangular element

(c) Dependent variables and their derivatives are continuous at inter-element boundaries

(d) 2^nddegree polynomial corresponds to 6 noded triangle

This question was posed to me by my school principal while I was bunking the class.

Enquiry is from Library of Elements and Interpolation Functions topic in division Interpolation Functions, Numerical Integration and Modelling Considerations of Finite Element Method

Answer 1

Correct option is (c) Dependent variables and their derivatives are continuous at inter-element boundaries

For explanation I would say: In Lagrange family elements the nodes are regularly placed everywhere on the grid i.e., they are uniformly spaced. The location of the terms in Pascal’s triangle gives the location of nodes in elements. Thus, Pascal’s triangle can be viewed as a triangular element. The derivatives of dependent variables are not continuous at inter-element boundaries. 2^nd-degree polynomial corresponds to 6 noded triangles.