Thank you very much for all the hints, especially the techniques manual!

I reviewed my mixed FE code and found out that the number of elements which is calculated from the number of nodes was 48.5. I rounded that off to the next integer ("floor"). And this caused in octave some in building up the coefficient matrix confusion that led to a kind of singular system.

Apparently freemat did not bother about that "wrong" number of elements and yielded correct results!

I changed my discretization (uneven number of nodes) and octave gave my accurate results too!

Without having found out, what exactly happened in octave through the "wrong" number of elements I am very lucky, to have a "running" octave system. As I assumed octave selects the appropriate matrix factorization depending on the properties of the matrix itself.

Hope you too have a spring sun shining through your window!

A numerical poem:
Now the fifth daughter on the twelfth night
Told the first father that things weren’t right
My complexion she said is much too white
He said come here and step into the light, he says hmm you’re right
Let me tell the second mother this has been done
But the second mother was with the seventh son
And they were both out on Highway 61
("Highway 61" by Robert Zimmerman 1964)