ufl team mailing list archive

[Harish Narayanan <harish.mlists@xxxxxxxxx>]

Martin Sandve Alnæs wrote:
> On Wed, Apr 15, 2009 at 9:44 PM, Harish Narayanan
> <harish.mlists@xxxxxxxxx> wrote:
>> I am trying to learn how to set up a simple non-linear problem using a
>> UFL form. In order to solve the following (the non-linear Poisson demo
>> in DOLFIN),
>>
>> - div[(1+u^2)*grad(u)] = f,
>>
>> does something like the following look like the right approach?
>>
>> element = FiniteElement("Lagrange", "triangle", 1)
>>
>> v = TestFunction(element)
>> u = TrialFunction(element)
>> f = Function(element)
>> U = Function(element)
>>
>> L = ((1 + U*U)*inner(grad(U), grad(v)) - f*v)*dx
>> a = derivative(L, U, u)
>>
>> I have not yet fully understood how derivative() functions.
>>
>> Harish
> 
> This looks right.
> 
> Alternative (equivalent) notation:
>   L = (1 + U**2)*dot(grad(U), grad(v))*dx - f*v*dx
>   a = derivative(L, U)
> 
> Unless you need the trial function u for something
> else, derivative can make one for you.
> That would only be the case if you linearize part
> of the form manually, something like:
>   a = derivative(L, U, u) + foo*u*v*dx

And just for closure, this appears to be the right form. I used it
instead of NonlinearPoisson.form in the DOLFIN demo and the compiled C++
demo converges quadratically.

Harish