[deal.II] Re: Relation between Solution Error Behavior and Polynomial Approximation Degree

2017-11-28 Thread seven 
I see. 

Thanks,
Jiaqi

在 2017年11月27日星期一 UTC-5下午6:31:54，Jaekwang Kim写道：
>
> No, I typically, calculate values itself and use MATLAB to draw plots. 
>
> Thanks,
>
> Jaekwang 
>
> On Monday, November 27, 2017 at 3:24:46 PM UTC-6, seven wrote:
>>
>> Hello Jaekwang,
>>
>> I am trying to generate some log-log plots, and wondering if you used the 
>> functions in deal.ii to generate the figure. If not, what did you use?
>>
>> Thanks,
>> Jiaqi
>>
>> 在 2016年9月29日星期四 UTC-4上午11:41:48，Jaekwang Kim写道：
>>>
>>>
>>> 
>>>
>>> Hi all, I have question on error behavior of FEM. 
>>>
>>> I thought that the order of error is O(h^p) where h is a mesh-size and p 
>>> is polynomial degree we use in approximation. 
>>>
>>> So, I thought that if I plot an error with number of mesh in log-log 
>>> scale, than the graph will show -p slope. 
>>> However, I the error behaves little bit different from my expectation.
>>>
>>> For example, I use a step7 tutorial program (which solves Helmholtz 
>>> decomposition and compares the FEM solution with exact solution.) 
>>>
>>> The error curve showed more steep slope whenever I increase polynomial 
>>> degree approximation however, the slope is not (-p). 
>>> I reached slope (-3) when I used fifth-degree polynomial 
>>> approximation...   
>>> You can check this behavior in attached picture. 
>>>
>>> Until now, I have considered, 
>>>
>>> 1. Mapping(From reference cell to real cell) degree (which is originally 
>>> set to 1 but I used higher mapping) 
>>> 2. Instead of Qgauss quadrature, I am using QgaussLobatto Quadrature for 
>>> any integration over cells. 
>>> 3. Shape function , again I tried to use QgaussLobatto node point for 
>>> this) 
>>>
>>> is there any suggestion that I need to fix more? 
>>> or my first prediction that the slope will show '-p' or error will just 
>>> behave O(h^p) was wrong?
>>>
>>> I am always thank you for all guys!
>>>
>>> Jaekwang Kim  
>>>
>>

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[deal.II] Re: Relation between Solution Error Behavior and Polynomial Approximation Degree

2017-11-27 Thread Jaekwang Kim 
No, I typically, calculate values itself and use MATLAB to draw plots. 

Thanks,

Jaekwang 

On Monday, November 27, 2017 at 3:24:46 PM UTC-6, seven wrote:
>
> Hello Jaekwang,
>
> I am trying to generate some log-log plots, and wondering if you used the 
> functions in deal.ii to generate the figure. If not, what did you use?
>
> Thanks,
> Jiaqi
>
> 在 2016年9月29日星期四 UTC-4上午11:41:48，Jaekwang Kim写道：
>>
>>
>> 
>>
>> Hi all, I have question on error behavior of FEM. 
>>
>> I thought that the order of error is O(h^p) where h is a mesh-size and p 
>> is polynomial degree we use in approximation. 
>>
>> So, I thought that if I plot an error with number of mesh in log-log 
>> scale, than the graph will show -p slope. 
>> However, I the error behaves little bit different from my expectation.
>>
>> For example, I use a step7 tutorial program (which solves Helmholtz 
>> decomposition and compares the FEM solution with exact solution.) 
>>
>> The error curve showed more steep slope whenever I increase polynomial 
>> degree approximation however, the slope is not (-p). 
>> I reached slope (-3) when I used fifth-degree polynomial approximation... 
>>   
>> You can check this behavior in attached picture. 
>>
>> Until now, I have considered, 
>>
>> 1. Mapping(From reference cell to real cell) degree (which is originally 
>> set to 1 but I used higher mapping) 
>> 2. Instead of Qgauss quadrature, I am using QgaussLobatto Quadrature for 
>> any integration over cells. 
>> 3. Shape function , again I tried to use QgaussLobatto node point for 
>> this) 
>>
>> is there any suggestion that I need to fix more? 
>> or my first prediction that the slope will show '-p' or error will just 
>> behave O(h^p) was wrong?
>>
>> I am always thank you for all guys!
>>
>> Jaekwang Kim  
>>
>

-- 
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[deal.II] Re: Relation between Solution Error Behavior and Polynomial Approximation Degree

2017-11-27 Thread seven 
Hello Jaekwang,

I am trying to generate some log-log plots, and wondering if you used the 
functions in deal.ii to generate the figure. If not, what did you use?

Thanks,
Jiaqi

在 2016年9月29日星期四 UTC-4上午11:41:48，Jaekwang Kim写道：
>
>
> 
>
> Hi all, I have question on error behavior of FEM. 
>
> I thought that the order of error is O(h^p) where h is a mesh-size and p 
> is polynomial degree we use in approximation. 
>
> So, I thought that if I plot an error with number of mesh in log-log 
> scale, than the graph will show -p slope. 
> However, I the error behaves little bit different from my expectation.
>
> For example, I use a step7 tutorial program (which solves Helmholtz 
> decomposition and compares the FEM solution with exact solution.) 
>
> The error curve showed more steep slope whenever I increase polynomial 
> degree approximation however, the slope is not (-p). 
> I reached slope (-3) when I used fifth-degree polynomial approximation... 
>   
> You can check this behavior in attached picture. 
>
> Until now, I have considered, 
>
> 1. Mapping(From reference cell to real cell) degree (which is originally 
> set to 1 but I used higher mapping) 
> 2. Instead of Qgauss quadrature, I am using QgaussLobatto Quadrature for 
> any integration over cells. 
> 3. Shape function , again I tried to use QgaussLobatto node point for 
> this) 
>
> is there any suggestion that I need to fix more? 
> or my first prediction that the slope will show '-p' or error will just 
> behave O(h^p) was wrong?
>
> I am always thank you for all guys!
>
> Jaekwang Kim  
>

-- 
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For mailing list/forum options, see 
https://groups.google.com/d/forum/dealii?hl=en
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