Virtual element method
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.
Introduction
The Virtual Element Method (VEM) is a technique for numerically approximating partial differential equations using generalised polygonal or polytopedral meshes. It is an extension of Mimetic Finite Differences (MFD) and Finite Element Methods (FEM).[1]
Basic Concepts
- Subdivides a domain into partitions similar to a Finite Element Method.
- Uses non-polynomial virtual that do not need to be calculated. [3]
References
- ↑ 1.0 1.1 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.
- ↑ 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.
- ↑ Sutton, O. J. (August 2017). "The virtual element method in 50 lines of MATLAB". Numerical Algorithms. 75 (4): 1141–1159. doi:10.1007/s11075-016-0235-3. ISSN 1017-1398.
Further reading
- Dassi, F. (2023). "Vem++, a c++ library to handle and play with the Virtual Element Method". arXiv:2310.05748 [math.NA].
- Beirão Da Veiga, Lourenço; Brezzi, Franco; Marini, L. Donatella; Russo, Alessandro (2023). "The virtual element method". Acta Numerica. 32: 123–202. doi:10.1017/S0962492922000095.
- The Virtual Element Method and its Applications. SEMA SIMAI Springer Series. 31. 2022. doi:10.1007/978-3-030-95319-5. ISBN 978-3-030-95318-8. Search this book on
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