Question

Which option is not correct concerning the bilinear term B(v,w) in the variational problem of the viscous fluid flow equation?

(a) It is symmetric

(b) It contains the viscosity matrix

(c) Bv(w,v)= Bv(v,w)

(d) It is bilinear in both w and v

The question was asked in an interview.

Question is from Penalty in portion Flows of Viscous Incompressible Fluids of Finite Element Method

Answer 1

Correct answer is (d) It is bilinear in both w and v

Explanation: The complete variational problem of the viscous fluid flow equation is Bt(w,v)+Bv(w,v)-B̅p(w,P)=l(w) and –Bp(w3, v)=0. The term, Bv(v,w) is linear in both v and w, it is symmetric because it contains the symmetric matrix, C. Thus Bv(w,v)= B(v,w). The variational problem Bv(v,w)=l(w) is a constrained problem.