Draft:Virtual element method

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Instructions · What links here · Virtual element method (talk: + · bio) · (log) · Copyvios report · reFill · Citation Bot · (Search: Google, Bing, Wikipedia) · Submitted 6 days ago by AHFrederiksen (talk: D · +) · Last edited 2 days ago by TakuyaMurata

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]