How to assign function at each time level and use it

1

Respected sir

Can you please help me in defining the function at each time level and use it to solve Variational form.

Define variational problem

u = TrialFunction(V)
v = TestFunction(V)
u0 = Function(V) # u_0
u1 = Function(V) # u_1
u2 = Function(V) # u_2
u0 = my_projection(u_D, V)# u_0
u1.assign(u0) # u_1
u2.assign(u0) # u_2

###“Here I want to assign function at each time level”
for n in range(num_steps):
u(n) = Function(V) # u_n
u(n).assign(u0) # u_n

print(u(n))

B1 = (u*v + dot(a*grad(u), grad(v)) )*dx
L1 = (u0 + k1*f)*v*dx

for n in range(num_steps):
    B2 = (u*v + dot(a*grad(u), grad(v)) )*dx
    L2 = f*v*dx
    L2 += (u1-u0)*v*dx


# Time-stepping
u = Function(V)
t = 0
for n in range(num_steps-1):

    # Update current time
    t += dt
    a.t = t
    b.t = t
    c.t = t
    u_D.t = t
    f.t = t
    # Compute solution
    #solve(a == L, u, bc)
    if n <  2:
        u0.assign(u1)
        solve(B1 == L1, u, bc)
        # Update previous solution
        u1.assign(u)
    else:

****“Here I want to use the assigned function at each time level”

        u0.assign(u(n-2))
        u1.assign(u(n-1))
        solve(B2 == L2, u, bc)
        # Update previous solution
        un.assign(u)
        u0.assign(u(n-1))
        u1.assign(u(n))