why step-24 result is more "angular" than step-89

[meng deng]

I trid the same initial value in step-24 as step-89, but step-89 is smoother than step-24, and step-89 needs less grids. I also set the fe.degree -> 3.

[meng deng]

for example, i created a 4 grids mesh with 3-order DGQ<2> in step-24, GaussPluse expression: exp(-1000 * ( (x-x0)^2 + (y-y0) ^ 2 )). 
distribution of the  quadrature points distribution of :

The initial value plot doesn't seem to have that many control points: 

[Wolfgang Bangerth]

On 11/29/24 22:10, meng deng wrote:
> I trid the same initial value in step-24 as step-89, but step-89 is smoother
> than step-24, and step-89 needs less grids. I also set the fe.degree -> 3.

Meng,
can you explain in more detail what it is you tried, and how the result you
get differs from your expectation? I have to admit that I do not understand
from your message (or the follow-up) what it is you ask about.

Best
WB

[meng deng]

thank you for your response, Prof. Wolfgang Bangerth.

In Step-24, I encountered numerical dispersion in my wave equation simulations at the beginning. I understand that this issue can often be mitigated by refining the mesh and reducing the time step. However, in the results of Step-89, even with a relatively coarse mesh, the numerical dispersion seems much smaller. It also appears that higher-order interpolation is applied, which is more in line with my expectations.

What I would like to understand is why Step-89 gives better results than Step-24. As mentioned earlier, in Step-24, the results appear to resemble linear interpolation, even though I used third-order finite elements. In contrast, Step-89 seems to produce results that behave more like higher-order interpolation. Additionally, I’ve noticed that the parameters of the `build_patches` function seem to have a significant impact on the output, which might explain some of the differences.

If my question is still unclear or confusing, I completely understand and I appreciate your time. Please feel free to ignore it if it’s not clear. I can reduce the time step as much as possible to minimize numerical dispersion. 

[Luca Heltai]

Could it be that you are not using higher order in the output result?

https://github.com/dealii/dealii/wiki/Notes-on-visualizing-high-order-output

L.

> On 30 Nov 2024, at 13:14, meng deng <dengm...@gmail.com> wrote:
>
> for example, i created a 4 grids mesh with 3-order DGQ<2> in step-24, GaussPluse expression: exp(-1000 * ( (x-x0)^2 + (y-y0) ^ 2 )).

> distribution of the quadrature points distribution of :<quad_points.png>
> The initial value plot doesn't seem to have that many control points: <initial_value.png>

>
>
> 在2024年11月30日星期六 UTC+8 13:10:20<meng deng> 写道：
> I trid the same initial value in step-24 as step-89, but step-89 is smoother than step-24, and step-89 needs less grids. I also set the fe.degree -> 3.
>
>

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> <quad_points.png><initial_value.png>