Question

In the penalty formulation of the fluid flow model, if the velocity field (vx, vy ) satisfies the continuity equation, then the weight functions (w1, w2) also satisfy the continuity equation.

(a) True

(b) False

This question was posed to me in an online quiz.

This intriguing question originated from Penalty topic in section Flows of Viscous Incompressible Fluids of Finite Element Method

Answer 1

The correct option is (b) False

To elaborate: In the penalty formulation, we begin with the unconstrained problem described by the weak forms of the mixed model, without the time—derivative terms. Now, suppose that the velocity field (vx, vy )  is such that the continuity equation is satisfied identically. Then the weight functions (w1, w2) being (virtual) variations of the velocity components, also satisfy the continuity equation.