# Which option is not correct about the Lagrange rectangular element used in FEM?

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Which option is not correct about the Lagrange rectangular element used in FEM?

(a) Second-order Lagrange element has nine nodes

(b) Zero-order Lagrange element has one node

(c) First-order Lagrange element has four nodes

(d) Third-order Lagrange element has fifteen nodes

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

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

## 1 Answer

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The correct option is (d) Third-order Lagrange element has fifteen nodes

The best I can explain: In general a p^th-order Lagrange rectangular element has n nodes with n= (p+1)^2, where p=0,1,2 …

For p=0,

n=1.

For p=1,

n=2^2,

=4.

For p=2,

n=3^2

=9.

For p=3,

n=4^2

=16.

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