Hi Yaqi
Thank you very much for your reply. Unfortunately, tutorial 28 can not help
me.
The equation is rather simple. My problem is how to preserve the mass during
the mesh
refinement. To be specified,
if I get the solution u_{n-1} at time n-1 on an "old" mesh, say T_{n-1}, and
I adaptively
refine the mesh to a new mesh T_n from the numerical solution u_{n-1}. Now I
want to
project u_{n-1} to the new refined mesh such that the mass is preserved,
i.e., the integration
of u_{n-1} on mesh T_{n-1} equal the integration of its projection on mesh
T_n.
How to define this projection is my question. Of course, there maybe other
better approach for
this problem. If you have other good idea to solve this 3-D transport
equation, please let me know.
Thank you again for your help.
Best,
Liang
On Tue, Oct 21, 2008 at 1:13 PM, Yaqi Wang <[EMAIL PROTECTED]> wrote:
> Hi Zhu,
>
> I guess you are dealing with a term in your equation which composes of
> variables defined on a different mesh from the mesh of the equation. If this
> is true, you may want to take a quick look on tutorial 28.
>
> I hope this helps.
>
> Regards,
> yaqi
>
> On Tue, Oct 21, 2008 at 2:20 PM, Zhu Liang <[EMAIL PROTECTED]> wrote:
>
>> Hi all
>>
>> Sorry for the re-post. As Ruhollah suggested, I would like to repeat my
>> question in detail.
>>
>> The equation I faced is a simple 3-D transport equation with smooth
>> initial condition on a relatively large domain \Omega:
>>
>> u_t + div(a u) =0
>>
>> In my analysis, u becomes singular as t goes to infinity. So I would like
>> to apply the adaptive finite element method (Crank-Nicolson scheme for time
>> discretization). My question is how to preserve the mass (\int_\Omega u dx
>> =const) during this approach.
>>
>> Basically, people apply the L^2- projection to transform numerical
>> solution u_{n-1} on an "old" mesh to a new refined mesh and make
>> the result the solution at time n-1. For this transport equation, I can
>> not use the L^2-projection as it violate the conservation law.
>>
>> Does anyone have some good ideas or suggestions for this case?
>>
>> Best,
>> Liang
>>
>> _______________________________________________
>>
>>
>
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