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In Finite Element Method (FEM), for discretization purpose in general, which 2D element is an undesired one?

(a) An equilateral triangle of side 5 units

(b) A quadrilateral

(c) A rhombus of side 10 units

(d) A rectangle of dimensions 100×1

I had been asked this question in an online quiz.

This intriguing question originated from Some Comments on Mesh Generation and Imposition of Boundary Conditions topic in section Single Variable Problems of Finite Element Method

1 Answer

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Best answer
The correct choice is (d) A rectangle of dimensions 100×1

Easy explanation: During discretization, when a mesh is made, care should be taken to avoid elements with very large aspect ratios (i.e. the ratio of one side of an element to the other) or small angles. In finite element equations the coefficient matrices depend on the aspect ratios. If the aspect ratios is very large, the resulting coefficient matrices are ill—conditioned (i.e., numerically not invertible).

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