[Libmesh-users] action of Lagrange multipliers

[Tobias M. <tob...@un...>]

Dear all,

I have some problem with Lagrange multipliers: Maybe I misinterpret my 
results, but somehow they don't have the effect I expected.

Looking at the solution of systems_of_equations_ex3, (using paraview) I 
see the (real part of) pressure r_p to be 0 at time step 0 and than it 
jumps to  ~10, where it stays for the rest of the simulation. But isn't 
it actually enforced to stay at 0 "forever"?

I also tried to change its value to some other fixed (and 
time-dependent) ones:

diff --git 
a/examples/systems_of_equations/systems_of_equations_ex3/systems_of_equations_ex3.C 
b/examples/systems_of_equations/systems_of_equations_ex3/systems_of_equations_ex3.C
index b626203..f576138 100644
--- 
a/examples/systems_of_equations/systems_of_equations_ex3/systems_of_equations_ex3.C
+++ 
b/examples/systems_of_equations/systems_of_equations_ex3/systems_of_equations_ex3.C
@@ -614,8 +614,15 @@ void assemble_stokes (EquationSystems & es,
            // negative one.  Here we do not.
            for (unsigned int i=0; i<n_p_dofs; i++)
              {
-              Kp_alpha(i,0) += JxW[qp]*psi[i][qp];
-              Kalpha_p(0,i) += JxW[qp]*psi[i][qp];
+              // original: set p=0
+              //Kp_alpha(i,0) += JxW[qp]*psi[i][qp];
+              //Kalpha_p(0,i) += JxW[qp]*psi[i][qp];
+              // lets fix the pressure to some finite value:
+              //Kp_alpha(i,0) += JxW[qp]*psi[i][qp]-1.*JxW[qp];
+              //Kalpha_p(0,i) += JxW[qp]*psi[i][qp]-1.*JxW[qp];
+              // lets make the pressure growing with time.
+              Kp_alpha(i,0) += JxW[qp]*psi[i][qp]-theta*dt*JxW[qp];
+              Kalpha_p(0,i) += JxW[qp]*psi[i][qp]-theta*dt*JxW[qp];
                for (unsigned int j=0; j<n_u_dofs; j++)
                  {
                    Kpu(i,j) += JxW[qp]*psi[i][qp]*dphi[j][qp](0);


However, even though the values change a bit, the general behaviour 
stays the same.

Could someone please help me clarifying, what is wrong here?

Thanks in advance,

Tobias