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In Finite Element Method (FEM), While domain discretization, at which of the following geometrical cases a node is not required?

(a) Change in cross-section area only

(b) Change in cross-section only

(c) Change in cross section area as well as change in cross-section

(d) No change

This question was addressed to me at a job interview.

Question is from Some Comments on Mesh Generation and Imposition of Boundary Conditions in section Single Variable Problems of Finite Element Method

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Correct option is (d) No change

Easy explanation: While domain discretization, a node is necessary to be placed whenever there is a geometric discontinuity. For example, a change in cross section area or change in cross-section or both.

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