Question

In the formulation of governing equations, which option does not signify the characteristics of a weight function?

(a) Weight functions are multiplied to governing equations to obtain weak forms

(b) Weight functions are interpreted from the physical setup of the problem

(c) Weight function must denote a non-dimensional quantity

(d) Weight function can be interpreted as a velocity

I got this question in an interview.

I'd like to ask this question from Velocity topic in division Flows of Viscous Incompressible Fluids of Finite Element Method

Answer 1

Right option is (c) Weight function must denote a non-dimensional quantity

The best I can explain: In the development of the weak form, we consider a typical element and multiply its governing equations with weight functions. They can be interpreted physically for a given equation; for example, in the momentum equation, the weight function must be interpreted as velocity. For the representing volume change, weight function is like pressure. Thus, it can be a dimensional quantity.