Re: [Libmesh-users] [RB] Min-theta approach

[David K. <dav...@ak...>]

On Sun, Apr 1, 2018 at 10:26 PM, <ss...@pu...> 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