[Dune] question: Virtual Element Methods

[Dedner, Andreas]

Dear Franco.
As Christoph already mentioned there is a dune module that covers some VEM in 2D. £D is sth i would like to work on
but currently I am not finding the time to do that. For some deatil and what currently is available have a look at
https://arxiv.org/abs/2208.08978
There is a page in our tutorial
https://www.dune-project.org/sphinx/content/sphinx/dune-fem/vemdemo_descr.html
which shows how to use the Vem spaces together with the available Python bindings to define the PDE and solve the problem (that uses UFL to define the model).
If you have a specific problem in mind let me know, happy to extend the code.
Regards
Andreas
________________________________
From: Dune <dune-bounces at lists.dune-project.org> on behalf of Christoph Grüninger <foss at grueninger.de>
Sent: 11 February 2025 16:52
To: Franco Dassi <franco.dassi at unimib.it>; dune at lists.dune-project.org <dune at lists.dune-project.org>
Subject: Re: [Dune] question: Virtual Element Methods

Hello Franco,
welcome to Dune!

Dune is a framework offering basic things like grid managers, linear
solvers, and local functions. On top of these core modules, other
modules add complete discretizations, physics and advanced methods.
Technically they are not part of Dune but are extensions supported by a
smaller set of people. Dune-FEM is such a discretization module and
there is a paper realizing Virtual Element Methods on top of that.

"A Framework for Implementing General Virtual Element Spaces"
Andreas Dedner, Alice Hodson, 2024
https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdoi.org%2F10.1137%2F23M1573653&data=05%7C02%7CA.S.Dedner%40warwick.ac.uk%7Cb52728b3609347674b5908dd4abc9f4d%7C09bacfbd47ef446592653546f2eaf6bc%7C0%7C0%7C638748896186483369%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=3cM5MotjaQKWjnNz7cymi1n6tm6RdT8VU2webox3j4Q%3D&reserved=0<https://doi.org/10.1137/23M1573653>

"Virtual element methods for fourth-order problems: implementation and
analysis"
Alice Hodson, PhD thesis, 2022

Further links to code repository:
> https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdune-project.org%2Fsphinx%2Fcontent%2Fsphinx%2Fdune-fem%2Fvemdemo_descr.html&data=05%7C02%7CA.S.Dedner%40warwick.ac.uk%7Cb52728b3609347674b5908dd4abc9f4d%7C09bacfbd47ef446592653546f2eaf6bc%7C0%7C0%7C638748896186508068%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=WivDNsbk9yKzMlz0KxdJOlAC79H48DqZyfej3vc%2FFhw%3D&reserved=0<https://dune-project.org/sphinx/content/sphinx/dune-fem/vemdemo_descr.html>

Andreas Dedner is a core developer and also reading the mailing list. He
might add to my email or be able to answer more detailed questions.

Bye
Christoph

--
Most customers will not accept source code with compile errors in it.
                  Dan Saks, CppCon 2016 (https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fyoutu.be%2FD7Sd8A6_fYU&data=05%7C02%7CA.S.Dedner%40warwick.ac.uk%7Cb52728b3609347674b5908dd4abc9f4d%7C09bacfbd47ef446592653546f2eaf6bc%7C0%7C0%7C638748896186521205%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=N4MsTD%2FahxFQtZF267D3j8PBbwh1NfJARATRc5TSfOk%3D&reserved=0<https://youtu.be/D7Sd8A6_fYU>)


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