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How compute norms for solution of time depend Stokes problem

0 votes

Hi,
I am interesting with time depend Stokes problem, and to solve this problem used Chorin projecton method. Now I would like to compute error estimate for the Time depend Stokes problem with initial velocity and homogeneous Dirichlet boundary conditions. For implementitation I used no-sleep condition for velocity and inflow and outflow Dirichlet conditions for pressure. Could somebody help me with computing next error estimate:
||u_exact - u_t||_l^∞([L^2(0mega)]^d) (Infinity norm based on L^2 norm)

Here is part of my code for this computing:
1. First I define L^2 norm:
def errornormL2(ue_fun, u_h, Ve):
u_h_Ve = interpolate(u_h, Ve)
u_e_Ve = interpolate(ue_fun, Ve)
e_Ve = Function(Ve)
e_Ve.vector()[:] = u_e_Ve.vector().array() - u_h_Ve.vector().array()
error = e_Ve**2*dx
return sqrt(assemble(error, mesh=Ve.mesh())), e_Ve
2. Then l^infinity in time loop:
Eu1_Linf = 0.0
ue_fun.t=t
Eu1_new, e_Ve = errornormL2(ue_fun, u1, V1)
Eu1_Linf = max(Eu1_new, Eu1_Linf)

here: V1 = VectorFunctionSpace(mesh, "Lagrange", 5)

and u1 is solution os given problem.
Thanks a lot in advance

asked Jul 29, 2014 by Gozel FEniCS Novice (140 points)

You should be more precise in what goes wrong. Or you have to provide some executable code. Btw., your problem seems very solvable with a bit of hacking. And, you may want to use the dolfin buit-in function errornorm. See here.

I used no-sleep condition ...

You should go sleeping ;-)

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