Do FeniCS programs only handle the PDE with even order derivatives?

Thank you very much.

Hello Garth,

Thank you for your answer last time.

I am still confused with the non self-adjoint PDEs. I tried to
construct the weak form, but when I compile it, it shows error saying
"ufl.log.UFLException: Shape mismatch in Sum".

I have attached the scanned problem description. It's a 1D
convection-diffusion equation: grad(u)-0.01*div grad(u)=0 with
Drichlet BCs: u(0)=1, u(1)=0

My question is how we should define the "a" function and let the code
run correctly?

I have tried:

a=(grad(u)*v-0.01*dot(grad(v),grad(u)))*dx
a=inner(grad(v),(u-0.01*grad(u)))*dx

But neither of them worked. I guess the du/dx*v term will cause a
non-symmetric coefficient matrix, that's what the shape mismatch mean.
Can you tell me how to solve it? I will really appreciate your help.

Thank you very much.

Regards,

Bin

On Thu, Jan 21, 2010 at 2:51 AM, Garth Wells
<email address hidden> wrote:
> Your question #98160 on FEniCS Project changed:
> https://answers.launchpad.net/fenics/+question/98160
>
>    Status: Open => Answered
>
> Garth Wells proposed the following answer:
>
> cutejeff wrote:
>> New question #98160 on FEniCS Project:
>> https://answers.launchpad.net/fenics/+question/98160
>>
>> I am the newcomer for Fenics, I just read the Tutorial. It seems like
>> it always needs to construct the weak form (at least true for the
>> examples in the tutorial). From the FEM course I have taken, I
>> remember  if the differential operator is non-self adjoint or
>> non-linear, then the weak form is variationally inconsistent,
>> therefore there is no unique solution for the weak form method.  If
>> this is true, then weak form shouldn't be considered for the PDE with
>> odd order derivatives or non-linear PDE.
>>
>
> Sounds like someone was leading you astray in the FEM course that you
> followed. For problems which are not self-adjoint, one can't pose them
> in terms of mimisation of a functional, but the weak form can still be
> formulated. Whether or not a particular equation has a unique requires
> analysis.
>
> There are plenty of demos in DOLFIN for non self-adjoint PDEs and for
> nonlinear problems,
>
> Garth
>
>
>> My last question is do fenics programs involve Least Squares Method?
>> or is it going to involve least squares process in future?
>>
>> Thank you.
>>
>
> --
> If this answers your question, please go to the following page to let us
> know that it is solved:
> https://answers.launchpad.net/fenics/+question/98160/+confirm?answer_id=0
>
> If you still need help, you can reply to this email or go to the
> following page to enter your feedback:
> https://answers.launchpad.net/fenics/+question/98160
>
> You received this question notification because you are a direct
> subscriber of the question.
>

It has nothing to do with non-symmetric matrices. There is something strange about the way you're writing your PDE (it only make sense in 1D). In general, grad(u) - dot(grad(v)*grad(u)) doesn't make sense as you are trying to subtract a scalar from a multi-component object. It is this "shape mismatch" that UFL is complaining about.

Try using u.dx(0) (the derivative of u along the x direction) instead of grad(u) and see if it helps in your code above. This way, you are explicitly telling the form compiler that what you really want is a derivative in one direction, not a gradient.

Now it works, Thanks a lot.