Discussion Closed This discussion was created more than 6 months ago and has been closed. To start a new discussion with a link back to this one, click here.

Typo in error estimation document?

Please login with a confirmed email address before reporting spam

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 dic 2021, 09:03 GMT-5
Magnus Ringh COMSOL Employee

Please login with a confirmed email address before reporting spam

Posted: 3 years ago 14 dic 2021, 08:20 GMT-5
Updated: 3 years ago 14 dic 2021, 08:20 GMT-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

Please login with a confirmed email address before reporting spam

Posted: 3 years ago 14 dic 2021, 08:52 GMT-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

Please login with a confirmed email address before reporting spam

Posted: 3 years ago 14 dic 2021, 08:59 GMT-5

Hi Sahil,

Yes, that's correct.

Magnus

Hi Sahil, Yes, that's correct. Magnus

Please login with a confirmed email address before reporting spam

Posted: 3 years ago 14 dic 2021, 09:03 GMT-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

Note that while COMSOL employees may participate in the discussion forum, COMSOL® software users who are on-subscription should submit their questions via the Support Center for a more comprehensive response from the Technical Support team.