A virtual element method for the acoustic vibration problem
| Autor: | Gonzalo Rivera, David Mora, Lourenço Beirão da Veiga, Rodolfo Rodríguez |
|---|---|
| Přispěvatelé: | BEIRAO DA VEIGA, L, Mora, D, Rivera, G, Rodríguez, R |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Discretization
65N25 70J30 010103 numerical & computational mathematics 01 natural sciences law.invention 65N30 65N25 70J30 76M25 law FOS: Mathematics Polygon mesh Mathematics - Numerical Analysis 0101 mathematics Mathematics 65N30 Rotor (electric) Applied Mathematics Numerical analysis Mathematical analysis Spectrum (functional analysis) 76M25 Order (ring theory) Numerical Analysis (math.NA) 010101 applied mathematics MAT/08 - ANALISI NUMERICA Computational Mathematics Scheme (mathematics) Virtual Elements eigenvalue problem Element (category theory) |
| Popis: | We analyze in this paper a virtual element approximation for the acoustic vibration problem. We consider a variational formulation relying only on the fluid displacement and propose a discretization by means of $$\mathrm {H}(\mathrm {div})$$H(div) virtual elements with vanishing rotor. Under standard assumptions on the meshes, we show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates. With this end, we prove approximation properties of the proposed virtual elements. We also report some numerical tests supporting our theoretical results. |
| Databáze: | OpenAIRE |
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