[petsc-users] snes options for rough solution

[Praveen C]

On Tue, Dec 13, 2016 at 2:50 AM, Matthew Knepley <knepley at gmail.com> wrote:

> On Mon, Dec 12, 2016 at 2:29 AM, Praveen C <cpraveen at gmail.com> wrote:
>
>> Hello Matt
>>
>> I have attached the detailed output.
>>
>> Fenics automatically computes Jacobian, so I think Jacobian should be
>> correct. I am not able to run the Fenics code without giving the Jacobian.
>> I am currently writing a C code where I can test this.
>>
>> This equation is bit weird. Its like this
>>
>> u_t = ( K u_x)_x
>>
>> K = u / sqrt(u_x^2 + eps^2)
>>
>
> I do not understand how to show parabolicity in this case. However, I have
> a more fundamental misunderstanding. In your code, I see
>
>   R0 = idt*(u-uold)*v*dx + K0*ux*vx*dx
>
> for the residual, which looks like
>
> R0 = u_t + K u_x
>
> to me. Where is the extra derivative you show above?
>
>
Hello Matt

vx is derivative of test function. So the last term is a second order
differential operator. The PDE in full looks like this

u_t = u_x^2/sqrt(u_x^2 + eps^2) + eps^2 * u * u_xx / (u_x^2 + eps^2)^1.5

With u > 0, the last term is parabolic. But numerically, I solve it in
divergence form.

Best
praveen
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