Question

Which option is not correct about the Lagrange family of triangular elements used in FEM?

(a) 2^nd-degree polynomial corresponds to 6 noded triangle

(b) 0^th-degree polynomial corresponds to 1 noded triangle

(c) 1^st-degree polynomial corresponds to 3 noded triangle

(d) 3^rd-degree polynomial corresponds to 9 noded triangle

This question was addressed to me in an interview.

My question is from Library of Elements and Interpolation Functions in section Interpolation Functions, Numerical Integration and Modelling Considerations of Finite Element Method

Answer 1

Correct option is (d) 3^rd-degree polynomial corresponds to 9 noded triangle

To explain: A p^th degree polynomial corresponds to n noded triangular element with n=0.5(p+2)(p+1), where n=0, 1, 2 …

For p=0,

n=1.

For p=1,

n=0.5*3*2,

=3.

For p=2,

n=0.5*3*4

=6.

For p=3,

n=0.5*4*5

=10.