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.

Perugia, I., Pietra, P., Russo, A. (2016). A plane wave virtual element method for the Helmholtz problem. MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE, 50(3), 783-808 [10.1051/m2an/2015066].

A plane wave virtual element method for the Helmholtz problem

RUSSO, ALESSANDRO
2016

Abstract

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.
Articolo in rivista - Articolo scientifico
Duality estimates; Error analysis; Helmholtz equation; Plane wave basis functions; Virtual element method;
Duality estimates; Error analysis; Helmholtz equation; Plane wave basis functions; Virtual element method
English
2016
50
3
783
808
none
Perugia, I., Pietra, P., Russo, A. (2016). A plane wave virtual element method for the Helmholtz problem. MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE, 50(3), 783-808 [10.1051/m2an/2015066].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/99675
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