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In FEM, which option is used to develop the Higher-order rectangular elements (i.e., rectangular elements with interpolation functions of higher degree) systematically?

(a) A rectangular array of binomial coefficients

(b) Galerkin method

(c) Jacobi method

(d) Delaunay triangulation

This question was posed to me in a national level competition.

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

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The correct answer is (a) A rectangular array of binomial coefficients

Explanation: Analogous to the Lagrange family of triangular elements, the Lagrange family of rectangular elements can be developed from a rectangular array of binomial coefficients. Since a linear rectangular element has four corners (hence, four nodes), the polynomial should have the first four terms 1, x, y, and xy(which form a parallelogram in Pascal’s triangle and a rectangle in the rectangular array of binomial coefficients).

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