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What is the reason for an element in the Serendipity family to have a smaller size of stiffness matrix compare to a similar element in the Lagrange family?

(a) Absence of interior nodes

(b) Modified element connectivity

(c) Lesser interpolation functions

(d) Irregular arrangements of nodes

The question was asked in a national level competition.

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

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Correct choice is (a) Absence of interior nodes

The best explanation: The internal nodes of the higher-order elements of the Lagrange family do not contribute to inter-element connectivity, and hence they are condensed out at element level; as a result, the size of the element matrices is reduced. However, the element connectivity remains unaffected. The elements formed after removing the internal nodes are called serendipity elements.

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