The mixed virtual element method on curved edges in two dimensions
| Autor: | Giuseppe Vacca, Anna Scotti, Alessio Fumagalli, Stefano Scialò, Franco Dassi, Davide Losapio |
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| Přispěvatelé: | Dassi, F, Fumagalli, A, Losapio, D, Scialò, S, Scotti, A, Vacca, G |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Curved edges
Curvilinear coordinates Computer science High order approximations Mechanical Engineering Mathematical analysis Computational Mechanics General Physics and Astronomy Boundary (topology) Numerical Analysis (math.NA) Mixed VEM Edge (geometry) High order approximation Space (mathematics) Curved edge Domain (mathematical analysis) Computer Science Applications Rate of convergence Mechanics of Materials Feature (computer vision) FOS: Mathematics Mathematics - Numerical Analysis ComputingMethodologies_COMPUTERGRAPHICS |
| Popis: | In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical feature, such as a portion of domain boundary or an internal interface , may introduce a geometrical error that degrades the expected order of convergence of the scheme. In the present work a suitable VEM approximation space is proposed to consistently handle curvilinear geometrical objects, thus recovering optimal convergence rates. The resulting numerical scheme is presented along with its theoretical analysis and several numerical test cases to validate the proposed approach. |
| Databáze: | OpenAIRE |
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