Question

Which option is not correct concerning the velocity variables, vx and vy in the weak form of the momentum and continuity equation?

(a) They are primary variables

(b) The minimum continuity requirement for interpolation is that they are linear in x and y

(c) The minimum continuity requirement for interpolation is that they are constant

(d) They are continuous across the inter-element boundary

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

My enquiry is from Velocity topic in division Flows of Viscous Incompressible Fluids of Finite Element Method

Answer 1

Right answer is (c) The minimum continuity requirement for interpolation is that they are constant

The best I can explain: In the weak form of the continuity equation, the boundary integral involving weight function is present by the use of integration by parts. It implies that vx and vy are primary variables; this, in turn, requires that vx and vy to be continuous across inter-element boundaries. The minimum continuity requirement for interpolation of vx and vy is that they are linear in x and y.