Solving nonlinear problem directly

On 15 March 2012 22:06, Gustav Kettil
<email address hidden> wrote:
> New question #190805 on DOLFIN:
> https://answers.launchpad.net/dolfin/+question/190805
>
> I'm trying to solve u'^2-u=0. u(0)=1, u(2)=4 with the built in solver but it does not converge. I have tried to use u_.vector()[:] = 1.0 as was suggested in another question but I'm not sure I put it in the right place. What to do?
>
> from dolfin import*
> mesh =Interval(50,0,2)
> V = FunctionSpace(mesh, 'Lagrange', 1)
>
> #boundary condition init.
> u0=Constant(1)
> def u0_boundary(x):
>   return x[0]<DOLFIN_EPS
>
> bc0 = DirichletBC(V, u0, u0_boundary)
>
> u2=Constant(4)
> def u2_boundary(x):
>   return abs(x[0]-2)<DOLFIN_EPS
>
> bc2 = DirichletBC(V, u2, u2_boundary)
>
> bcs=[bc0, bc2]
>
> # Define variational problem
> u  = TrialFunction(V)
>
> v  = TestFunction(V)
> u_ = Function(V)      # the most recently computed solution
>
> F  = inner(grad(u)*grad(u)-u, v)*dx
> F  = action(F, u_)

You must define the nonlinear residual form in terms of the Function:

F  = inner(grad(u_)*grad(u_)-u_, v)*dx

The rest looks fine at a glance.

Martin

> J  = derivative(F, u_, u)
>
> u_.vector()[:] = 1.0
>
> problem = NonlinearVariationalProblem(F, u_, bc2, J)
> solver  = NonlinearVariationalSolver(problem)
> solver.solve()
>
> plot(u_,title="u")
>
> interactive()
>
> --
> You received this question notification because you are a member of
> DOLFIN Team, which is an answer contact for DOLFIN.