Question

Concerning triangular elements in FEM, which option is not correct about the mathematical formula of Pascal’s triangle?

(a) It contains the terms in two coordinates only

(b) The position of the terms can be viewed as the nodes of a triangular element

(c) The position of the first and last terms of a row is at the vertices of a triangular element

(d) A triangular element of order 2 corresponds to the second row

The question was posed to me during a job interview.

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

Answer 1

The correct answer is (d) A triangular element of order 2 corresponds to the second row

The explanation: A Pascal’s triangle contains the terms of polynomials of various degrees in two coordinates. We can view the positions of the terms as nodes of a triangular element, with the constant term and the first and last terms of a given row being the vertices of the triangle. A triangular element of order 2 (i.e., the degree of the polynomial is 2) contains six nodes and corresponds to the third row of Pascal’s triangle.