Reference on "Solving a Laplace problem Using mean value constraints"

[ztdep...@gmail.com]

In step 11, Solving a Laplace problem with higher order mappings. Using mean value constraints. 

Could you please provide some references about the implementation process. 

[Wolfgang Bangerth]

Can you explain what specifically you're looking for?
Best
W.

--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[ztdepyahoo]

I am looking for the theory guide of the "mean value constraints " method in fem. 

	ztdepyahoo
ztdep...@gmail.com

---- Replied Message ----

From	Wolfgang Bangerth<bang...@colostate.edu>
Date	8/26/2022 23:46
To	<dea...@googlegroups.com>
Subject	Re: [deal.II] Reference on "Solving a Laplace problem Using mean value constraints"

--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en
---
You received this message because you are subscribed to a topic in the Google Groups "deal.II User Group" group.
To unsubscribe from this topic, visit https://groups.google.com/d/topic/dealii/i8EChiv8y98/unsubscribe.
To unsubscribe from this group and all its topics, send an email to dealii+un...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/89f9f0aa-de91-4011-903c-c537cd8f502b%40colostate.edu.

[Wolfgang Bangerth]

On 8/26/22 20:54, ztdepyahoo wrote:
> I am looking for the theory guide of the "mean value constraints " method in fem.

I think you need to try to be more detailed in your questions :-)

Regardless, I don't have much to offer. I think what the program does is how
every finite element professional would implement this, though I cannot point
to anything anyone has ever written about it.

If you are asking about the theory of imposing a mean value constraint, I
don't have anything to offer there either. The closest thing I can think of is
the "electrode model" in electrical impedance tomography (EIT) modeling, and
how it imposes a specific kind of constraint on parts of the boundary. There
is a substantial literature that considers the correct formulation, weak
formulation, and uniqueness/existence. You might be able to glean something
from there about the case here.