On Tue, Apr 3, 2018 at 4:58 AM, <ss.k...@pusan.ac.kr> wrote: > 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. >
This follows from the definition of the coercivity constant. Set trial and test function to be the same in the convection-diffusion bilinear form, and integrate the convection term by parts and you end up with a term that includes the divergence of the velocity field. If the velocity field is divergence-free, then that term vanishes. David *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> 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 ------------------------------------------------------------------------------ Check out the vibrant tech community on one of the world's most engaging tech sites, Slashdot.org! http://sdm.link/slashdot _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
