A PLANE WAVE VIRTUAL ELEMENT METHOD FOR THE HELMHOLTZ PROBLEM

被引：93
|
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
收藏
页码：783 / 808
页数：26
相关论文
共 50 条
  • [31] On the neumann problem for the Helmholtz equation in a plane angle
    Zhevandrov, P
    Merzon, A
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2000, 23 (16) : 1401 - 1446
  • [32] Plane wave approximation of homogeneous Helmholtz solutions
    Moiola, A.
    Hiptmair, R.
    Perugia, I.
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2011, 62 (05): : 809 - 837
  • [33] Plane wave approximation of homogeneous Helmholtz solutions
    A. Moiola
    R. Hiptmair
    I. Perugia
    Zeitschrift für angewandte Mathematik und Physik, 2011, 62
  • [34] The Goursat problem for a generalized Helmholtz operator in the plane
    Peter Ebenfelt
    Hermann Render
    Journal d'Analyse Mathématique, 2008, 105 : 149 - 167
  • [35] Investigation of a spectral problem for the Helmholtz operator on the plane
    E. M. Karchevskii
    S. I. Solov’ev
    Differential Equations, 2000, 36 : 631 - 634
  • [36] Investigation of a spectral problem for the Helmholtz operator on the plane
    Karchevskii, EM
    Solov'ev, SI
    DIFFERENTIAL EQUATIONS, 2000, 36 (04) : 631 - 634
  • [37] The Goursat problem for a generalized Helmholtz operator in the plane
    Ebenfelt, Peter
    Render, Hermann
    JOURNAL D ANALYSE MATHEMATIQUE, 2008, 105 (1): : 149 - 167
  • [38] A posteriori virtual element method for the acoustic vibration problem
    Lepe, F.
    Mora, D.
    Rivera, G.
    Velasquez, I.
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2023, 49 (01)
  • [39] THE INTERIOR PENALTY VIRTUAL ELEMENT METHOD FOR THE BIHARMONIC PROBLEM
    Zhao, Jikun
    Mao, Shipeng
    Zhang, Bei
    Wang, Fei
    MATHEMATICS OF COMPUTATION, 2023, 92 (342) : 1543 - 1574
  • [40] A VIRTUAL ELEMENT METHOD FOR THE VIBRATION PROBLEM OF KIRCHHOFF PLATES
    Mora, David
    Rivera, Gonzalo
    Velasquez, Ivan
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2018, 52 (04): : 1437 - 1456
12345