Re: [Libmesh-users] [RB] Question about a poseteriori error estimation

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

On Mon, Oct 15, 2018 at 4:30 AM <ss...@pu...> wrote:

> Thank you for your reply, but I still have not solved my problem.
>
> My questions seemed to be something wrong, so I want to ask again about a
> posteriori error estimation.
>
>
>
> According to “Reduced Basis Approximation and A Posteriori Error
> Estimation for Parameterized Partial Differential Equations” by Anthony T.
> Patera and Gianluigi Rozza, there are two error estimators, (i) energy-norm
> error bounds and (ii) X-norm error bounds.
>
>
>
> I think that these estimators are related to the variable
> “abs_error_bound” in the “Real RBEvaluation::rb_solve(unsigned int N)” code.
>
> Here I do not know if “abs_error_bound” is energy-norm error bounds or
> X-norm error bounds.
>
> This is the original question I intended in the first email.
>
>
>
> I am always thankful for your kind answers, David.
>

You can do either (i) or (ii), it's up to you. The difference between (i)
and (ii) is just related to which norm (and inner product) you're using.
The libMesh RB code makes no assumption about which inner product/norm you
want to use, so you can choose the inner product to implement either (i) or
(ii), but you have to specify that yourself.

If you set your inner product to be the "energy" inner product (by defining
inner product assembly so that it matches the system that you're solving at
a particular parameter) then you'll get option (i). I don't remember what
the "X-norm" refers to in that paper, but I guess you can do that too by
setting the inner product appropriately.

Best,
David