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

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

On Fri, Oct 12, 2018 at 2:58 AM <ss...@pu...> wrote:

> Hello, all.
>
>
>
> I have a question about the RB error estimation in LibMesh.
>
>
>
> I know that the maximum error bound is computed in the function
> "RBConstruction::compute_max_error_bound()."
>
> Here we should compute the "dual norm of residual" using the function
> "compute_residual_dual_norm(N)."
>
> But I do not know exactly if this "dual norm of residual" is "X-norm" or
> "energy-norm," where "X-norm" is parameter-independent and "energy-norm" is
> parameter-dependent.
>

The norm that is used is specified by the user. For example, in
reduced_basis_ex1, we set the inner product in SimpleRBConstruction to be
the "A0" operator (and the inner product is used to generate the norm). So
the inner-product and norm that is used is completely up to you.

Note, though, that the inner product must be parameter independent. This is
necessary since we don't want to change the inner product when we change
parameters.



> When I looked at the "compute_residual_dual_norm(N)" code, the current
> parameter is called by the "const RBParameters & mu = get_parameters();"
> code line.
>
> So I guess the "dual norm of residual" is the "energy-norm," and I would
> like to ask if it is correct.
>

No, the residual is whatever is specified by the user by calling
"set_inner_product_assembly". The parameter is used to evaluate the dual
norm in any specific case, but that is not related to the inner product
that is used.

Best,
David