Thank you for your reply, David.

 

I understood the answer as follows: ThetaA1 and ThetaA2 can be neglected in 
calculating the coercivity lower bound due to the divergence-free convection 
field.

However, I am not familiar with the field of thermal fluid engineering, so I do 
not know in detail why it can be ignored.

 

Could you tell me more about this problem with formulations of the lower bound 
and the divergence-free convection field? 

Or can you tell me about references related to this problem?

 

I always appreciate your help.

 

Regards,

SKang

 

From: David Knezevic <david.kneze...@akselos.com> 
Sent: Monday, April 2, 2018 8:34 PM
To: 강신성 <ss.k...@pusan.ac.kr>
Cc: libmesh-users <libmesh-users@lists.sourceforge.net>
Subject: Re: [Libmesh-users] [RB] Min-theta approach

 

On Sun, Apr 1, 2018 at 10:26 PM, <ss.k...@pusan.ac.kr 
<mailto:ss.k...@pusan.ac.kr> > wrote:

Hello, all.



I try to derive an RB error bound using the min-theta approach.

First of all, I saw the RB example 1 because this example shows the value of
coercivity constant lower bound, not dummy value.

However, this example does not satisfy requirements of the min-theta
approach.



If so, how was the lower bound value of the example 1 obtained?

I do not know why the lower bound value is 0.05 in the RB example 1.

 

 

If I recall correctly, the ThetaA1 and ThetaA2 are irrelevant to the coercivity 
constant because they give a divergence-free convection field (it's clearly 
divergence free since the field is constant everywhere, given by the parameters 
x_vel and y_vel). As a result we can set the coercivty lower bound to be the 
value returned by ThetaA0, which is 0.05.

 

Of course, this is a simple case, and in general one must use SCM to get the 
coercivity lower bound. I would say that in practice a lot of people are 
satisfied with skipping the SCM and just setting a dummy value (e.g. 1) for the 
coercivity lower bound. This means that the error bound isn't rigorous anymore, 
but it's still useful as an error indicator.

 

David

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