Journal
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
Volume 50, Issue 3, Pages 783-808Publisher
EDP SCIENCES S A
DOI: 10.1051/m2an/2015066
Keywords
Helmholtz equation; virtual element method; plane wave basis functions; error analysis; duality estimates
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Funding
- Italian Ministry of Education, University and Research (MIUR) [PRIN-2012HBLYE4]
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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.
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