A PLANE WAVE VIRTUAL ELEMENT METHOD FOR THE HELMHOLTZ PROBLEM

被引：96

作者：

Perugia, Ilaria ^{[1
,2
]}

Pietra, Paola ^{[3
]}

Russo, Alessandro ^{[4
]}

机构：

[1] Univ Vienna, Fac Math, A-1090 Vienna, Austria

[2] Univ Pavia, Dept Math, I-27100 Pavia, Italy

[3] CNR, Ist Matemat Appl & Tecnol Informat Enrico Magenes, I-27100 Pavia, Italy

[4] Univ Milano Bicocca, I-20126 Milan, Italy

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2016年 / 50卷 / 03期

关键词：

Helmholtz equation; virtual element method; plane wave basis functions; error analysis; duality estimates; DISCONTINUOUS GALERKIN METHODS; WEAK VARIATIONAL FORMULATION; LINEAR ELASTICITY PROBLEMS; LAGRANGE MULTIPLIERS; POLYGONAL MESHES; EQUATION; TREFFTZ; ACOUSTICS; VERSION; BOUNDS;

D O I：

10.1051/m2an/2015066

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：783 / 808

页数：26

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