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Typo in error estimation document?

Posted 14 déc. 2021, 07:31 UTC−5 Mesh, Parameters, Variables, & Functions, Studies & Solvers 4 Replies

Sahil Maharaj
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Hi!

I'm doing some work on error estimation, and I've been using this page as a reference: https://doc.comsol.com/5.5/doc/com.comsol.help.comsol/comsol_ref_solver.27.014.html

There's just one htis that's confusing me. Equation 20.1 is . But in the next line when referring to that equation it says, "the primal approximate solution, is defined by a variational formulation".

What confuses me is that this doesn't appear in the intial equation. Was it meant to say ? Or is the original equation wrong? Or is this a new piece of information not from the original equation? Thanks for your help.

4 Replies Last Post 14 déc. 2021, 09:03 UTC−5
Magnus Ringh COMSOL Employee

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Posted: 3 years ago 14 déc. 2021, 08:20 UTC−5
Updated: 3 years ago 14 déc. 2021, 08:20 UTC−5

Hi Sahil,

Unfortunately, there are some inconsistencies in the section about the error estimation theory in version 5.5. These parts of the documentation has been improved and revised in the upcoming COMSOL Multiphysics version 6.0. In this equation (where the min operator is not needed, and the text that you refer to has been removed), is the exact primal solution, is the finite-element approximation of , is the weak residual of the problem, is the exact dual solution corresponding to , and is the finite-element approximation of .

Best regards,

Magnus

Hi Sahil, Unfortunately, there are some inconsistencies in the section about the error estimation theory in version 5.5. These parts of the documentation has been improved and revised in the upcoming COMSOL Multiphysics version 6.0. In this equation (where the `min` operator is not needed, and the text that you refer to has been removed), u is the exact primal solution, u_{h} is the finite-element approximation of u, \rho is the weak residual of the problem, z is the exact dual solution corresponding to J, and z_{h} is the finite-element approximation of z. Best regards, Magnus
Sahil Maharaj
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Posted: 3 years ago 14 déc. 2021, 08:52 UTC−5

Hi Magnus,

Thanks for the speedy reply. Much appreciated for the help, it's really useful. So just to clarify, equation 20.1 should be presented as such: ?

Regards, Sahil

Hi Magnus, Thanks for the speedy reply. Much appreciated for the help, it's really useful. So just to clarify, equation 20.1 should be presented as such: J(u)-J(u_h)=J(e)=\rho (u_h,z-z_h) ? Regards, Sahil
Magnus Ringh COMSOL Employee

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Posted: 3 years ago 14 déc. 2021, 08:59 UTC−5

Hi Sahil,

Yes, that's correct.

Magnus

Hi Sahil, Yes, that's correct. Magnus
Sahil Maharaj
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Posted: 3 years ago 14 déc. 2021, 09:03 UTC−5

Ah, I see. That's perfect, thans so much for your help

Ah, I see. That's perfect, thans so much for your help

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