Hello,
thank you for your help. A quick internet search for "Finite Elements"+Mesh+Spiders did not produce any relevant hits - only models of mechanical structures called "spiders", or comparison "mesh" ="spider web". Nor are they mentioned in the dissertation that you have referenced. Is it a common terminology?
For now I am producing mesh by myself, using hexahedral elements, following some examples from "Element Mesh Generation" guide. While still not perfect, it is an improvement.
One interesting thing I noticed is that same code that produces that square in ver. 10.3 DOES NOT produce square in ver. 10.0. I am going to investigate deeper - is it a difference between versions or between computers (the two versions of Mathematica are installed on different computers). However, if I try to NDSolve in ver. 10.0 (under Windows 10), the kernel just quits (the appropriate MathKernel.exe disappears from the task list). This never happened to me before and I am not sure what to make of it. Perhaps I'll start a different thread here somewhere.