Question

In Finite Element Method (FEM), choose the incorrect option regarding to the dimensions (mm) of elements in a finite element mesh?

(a) Elements with very large aspect ratios are avoided

(b) Elements with small angles are undesired

(c) The coefficient matrices in finite element equations depend on dimensions of elements

(d) Rectangular elements with high aspect ratio are preferred

This question was posed to me in class test.

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

Answer 1

The correct choice is (d) Rectangular elements with high aspect ratio are preferred

To explain I would say: 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).