Is mesh orthogonality important for FEM?

Question

While studying mesh quality metrics in literature and software documentation, I've seen discussions about mesh orthogonality in Finite Volume Method (FVM) contexts, but not for Finite Element Method (FEM). For FEM, the metrics generally discussed and evaluated are skewness, smoothness and aspect ratio, for example.
This made me wonder: is mesh orthogonality also important for FEM?

EDIT: I will clarify my question by presenting the definition of orthogonality that I'm referring to. For two quadrilateral elements such as

the orthogonality angle $theta$ is the angle between the vector that connects the centroids of the elements $textbf{d}$ and the vector normal to the surface connecting the elements $textbf{n}$.

Wolfgang Bangerth · Accepted Answer

Yes. The constants that appear in the interpolation estimates upon which finite element error estimates are based contain minimum and maximum angles of triangles/tetrahedra (or similar geometric measures for quadrilaterals/hexahedra). These constants are smallest whenever you have equilateral triangles or square quadrilaterals.

Correct answer by Wolfgang Bangerth on July 27, 2021

alephzero · Answer

It depends on the problem being solved and the element formulation.
The orthogonality criterion you state may not be as important as the shape of each element.
For example in structural mechanics, with an irregular (e.g. automatically generated and refined) mesh and isoparametric elements, an important criterion for accuracy is the largest angle between sides meeting at a node.
A "very thin" triangle with angles of 89, 89 and 2 degrees is pretty harmless (but not very efficient since it doesn't occupy much area), but a "reasonable looking" triangle with angles 120, 30, and 30 is significantly worse than a triangle which is close to equilateral (or rather equiangular).

Is mesh orthogonality important for FEM?

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