Question

In the formulation of the finite element model for fluids flows, which option is not correct about the penalty formulation?

(a) The continuity equation is an additional relation among the velocity components

(b) The constraint is satisfied in an approximate sense

(c) Uses the penalty function method

(d) Involves natural and direct formulation of momentum and continuity equations

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

The query is from Governing Equations in portion Flows of Viscous Incompressible Fluids of Finite Element Method

Answer 1

The correct answer is (d) Involves natural and direct formulation of momentum and continuity equations

To elaborate: There are two different finite element models of momentum and continuity equations. The penalty formulation is based on the interpretation that the continuity equation is an additional relation among the velocity components. The constraint is satisfied in a least-squares (i.e., approximate) sense. This particular method of including the constraint in the formulation is known as the penalty function method. It does not involve the natural and direct formulation of momentum and continuity equations.