Largest eigenvalue of the stiffness matrix

Question

I implemented a Delaunay trianglular mesh generator, then I would like justify my chose about the Delaunay method. Then I survey about meshes. I found the next text:

There are 3 criteria about linear triangular finite elements (SHEWCHUK, 2002):

1. Interpolation Error: (elements of big sizes increase the error)
2. Gradiente Interpolation Error: (elements of big sizes and big angles increase the error)
3. Largest eigenvalue Condition of the stiffness matrix: little angles increase the error.

Someone can explain me that condition about the Largest Eigenvalue of Stiffness Matrix. Why is this the 3rd criteria a criteria for meshs? How is explained that criteria. And finally why little angles increase the error?

Answer 1

(3) It influences the condition number of the stiffness matrix, which you want to have small for the application of iterative solution methods.

(1)(2) If you look into interpolation error estimates, you find that these depend on the diameter $h_K$ of a triangle and on the radius $r_K$ of the incircle. You want to have $h_K$ small, and $\frac{h_K}{r_K}$ as small as possible. This ratio is large if $K$ has one very small or one very large angle.