The Fundamental Physical Bases of the WR Approach (and, Consequently, of FEM) in General
It has been quite some time (more than 1.5 years) that I had touched upon the topic of the physical bases of FEM in general, and of the general weighted residual (WR) approach in particular, at iMechanica (see here).
The position I then took was that there is no known physical basis at all for the WR approach---despite its loving portrayals in mathematical terms, or its popularity.
Further, I had also expressed (here and elsewhere) that a basis in physical principles existed for FEM only in a rather limited sense: wherever the energy interpretation was available for the model. (Note, this too is already at variance with what some of the authors have written in books.)
I have not yet changed my opinions.
But, still, it is easy to miss things.
And, it is easy to teach wrong things to one's students too---especially if doing so suits one's own professional goals, research programs, reputation, funding applications in the pipeline, greencard/citizenship applications, or a precisely similar set of things for one's PhD advisor/professional mentor/current superior/group/past alumni associates (sentimental in nature or otherwise).
Nevertheless, I would consider myself immoral if I did not check things out before proceeding to profess or teach them (or create some impression in my students' minds about them---positive or negative).Accordingly, here we go.
Please let me know if anyone has been able to unearth or discover any physical basis whatsoever---i.e. any explanation in terms of any known (or newly discovered) physical principles---over the past 1.5 years (or anytime earlier) whereby the weighted residual approach can be said to possess a fundamental physical interpretation.
And, thereby, also FEM, in its more general "avatar."
Thanks in advance.