A plane wave virtual element method for the Helmholtz problem

We introduce and analyze a virtual element method (VEM) for the Helmholtz problem with approximating spaces made of products of low order VEM functions and plane waves. We restrict ourselves to the 2D Helmholtz equation with impedance boundary conditions on the whole domain boundary. The main ingred...

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Bibliographic Details
Published inESAIM. Mathematical modelling and numerical analysis Vol. 50; no. 3; pp. 783 - 808
Main Authors Perugia, Ilaria, Pietra, Paola, Russo, Alessandro
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.05.2016
Subjects
35J05
65N12
65N15
65N30
Apexes
Basis functions
Boundary conditions
duality estimates
error analysis
Helmholtz equation
Helmholtz equations
Mathematical analysis
Nonlinear programming
plane wave basis functions
Plane waves
virtual element method
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Summary:We introduce and analyze a virtual element method (VEM) for the Helmholtz problem with approximating spaces made of products of low order VEM functions and plane waves. We restrict ourselves to the 2D Helmholtz equation with impedance boundary conditions on the whole domain boundary. The main ingredients of the plane wave VEM scheme are: (i) a low order VEM space whose basis functions, which are associated to the mesh vertices, are not explicitly computed in the element interiors; (ii) a proper local projection operator onto the plane wave space; (iii) an approximate stabilization term. A convergence result for the h-version of the method is proved, and numerical results testing its performance on general polygonal meshes are presented.
Bibliography:PII:S0764583X15000667
istex:8E52794234D60373162A9EE8E29EC28867BDB5DB
publisher-ID:m2an150076
ilaria.perugia@univie.ac.at
ark:/67375/80W-H6N56DXS-C
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2015066