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Finite Element Method
In Finite Element Method (FEM), for...

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

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+2 votes

asked Jan 30, 2022 in Finite Element Method by Ava (110k points)

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

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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

finite element method
single variable problems
some comments on mesh generation and imposition of boundary conditions

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1 Answer

+1 vote

answered Jan 30, 2022 by James (185k points)
selected Feb 3, 2022 by Ava

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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