Draft:Virtual element method

Submission declined on 27 September 2024 by Ldm1954 (talk).

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This draft has not been edited in over six months and qualifies to be deleted per CSD G13.

Declined by Ldm1954 10 months ago. Last edited by Ldm1954 10 months ago. Reviewer: Inform author.

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Comment: You have to find independent sources, and ones which are well cited. This is WP:TOOSOON, you probably have to wait for 2-3 years until there are > 100 cites of the papers. Ldm1954 (talk) 01:37, 27 September 2024 (UTC)

The Virtual Element Method (VEM) is a numerical technique used for solving partial differential equations (PDEs)^[1]^[2]. It is a generalization of the Finite Element Method (FEM) and is particularly noted for its flexibility in handling complex geometries.

VEM allows the use of general polygonal and polyhedral meshes, accommodating elements with any number of sides. This flexibility simplifies the meshing process for intricate geometries. The method draws inspiration from Mimetic Finite Difference schemes, which aim to replicate the properties of differential operators at the discrete level. Additionally, VEM supports high polynomial degrees, enhancing the accuracy of the solutions.

References

^ BeirãO Da Veiga, L.; Brezzi, F.; Cangiani, A.; Manzini, G.; Marini, L. D.; Russo, A. (January 2013). "Basic Principles of Virtual Element Methods". Mathematical Models and Methods in Applied Sciences. 23 (1): 199–214. doi:10.1142/S0218202512500492. ISSN 0218-2025.
^ Veiga, Lourenço Beirão Da; Brezzi, Franco; Marini, L. Donatella; Russo, Alessandro (May 2023). "The virtual element method". Acta Numerica. 32: 123–202. doi:10.1017/S0962492922000095. ISSN 0962-4929.

[1] BeirãO Da Veiga, L.; Brezzi, F.; Cangiani, A.; Manzini, G.; Marini, L. D.; Russo, A. (January 2013). "Basic Principles of Virtual Element Methods". Mathematical Models and Methods in Applied Sciences. 23 (1): 199–214. doi:10.1142/S0218202512500492. ISSN 0218-2025.

[2] Veiga, Lourenço Beirão Da; Brezzi, Franco; Marini, L. Donatella; Russo, Alessandro (May 2023). "The virtual element method". Acta Numerica. 32: 123–202. doi:10.1017/S0962492922000095. ISSN 0962-4929.

[1]

[2]