The nonconforming virtual element method for eigenvalue problems
| Autor: | Gianmarco Manzini, Giuseppe Vacca, Francesca Gardini |
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| Přispěvatelé: | Gardini, F, Manzini, G, Vacca, G |
| Rok vydání: | 2018 |
| Předmět: |
Numerical Analysis
Applied Mathematics Spectrum (functional analysis) 010103 numerical & computational mathematics Numerical Analysis (math.NA) Eigenfunction 01 natural sciences 010101 applied mathematics Computational Mathematics Rate of convergence nonconforming virtual element eigenvalue problem polygonal meshes Large set (Ramsey theory) Modeling and Simulation Product (mathematics) Convergence (routing) FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 0101 mathematics Element (category theory) Analysis Eigenvalues and eigenvectors Mathematics |
| DOI: | 10.48550/arxiv.1802.02942 |
| Popis: | We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allows to treat in the same formulation the two- and three-dimensional case. We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of theL2-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problem. The proposed schemes provide a correct approximation of the spectrum, in particular we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice. |
| Databáze: | OpenAIRE |
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