Question

Which option is not correct concerning the pressure variable, P in the weak form of the momentum and continuity equation?

(a) P is a primary variable

(b) P is a part of the secondary variables

(c) P=constant is the minimum continuity requirement for interpolation

(d) It is discontinuous across inter-element boundaries

The question was posed to me in a national level competition.

This intriguing question comes from Velocity topic in section Flows of Viscous Incompressible Fluids of Finite Element Method

Answer 1

Right option is (a) P is a primary variable

The best I can explain: In the weak form of the continuity equation, there is no boundary integral involving weight function because no integration by parts is used, this implies that P is not a primary variable; it is a part of the secondary variables, this, in turn, requires that P not be made continuous across inter-element boundaries. The minimum continuity requirement for interpolation of P is that P=constant.