Plane Wave Discontinuous Galerkin Methods: Exponential Convergence of the hp-Version

被引：0

作者：

Hiptmair, R. ^{[1
]}

Moiola, A. ^{[2
]}

Perugia, I. ^{[3
,4
]}

机构：

[1] ETH, Seminar Appl Math, CH-8092 Zurich, Switzerland

[2] Univ Reading, Dept Math & Stat, Reading RG6 6AX, Berks, England

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

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

来源：

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS | 2016年 / 16卷 / 03期

关键词：

Helmholtz equation; Approximation by plane waves; Trefftz-discontinuous Galerkin method; hp-version; A priori convergence analysis; Exponential convergence; WEAK VARIATIONAL FORMULATION; 2ND-ORDER ELLIPTIC PROBLEMS; FINITE-ELEMENT METHOD; HELMHOLTZ-EQUATION; P-VERSION; ACOUSTIC SCATTERING; DGFEM; STABILITY; DOMAINS; MESHES;

D O I：

10.1007/s10208-015-9260-1

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

引用

页码：637 / 675

页数：39

共 42 条

[1]

Abramowitz M., 2013, Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables, V(eds)

[2]

[Anonymous], 2008, TEXTS APPL MATH

[3] THE H-P VERSION OF THE FINITE-ELEMENT METHOD FOR DOMAINS WITH CURVED BOUNDARIES [J].

BABUSKA, I ;

GUO, BQ .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1988, 25 (04) :837-861

[4]

Babuska I, 1997, INT J NUMER METH ENG, V40, P727, DOI 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO

[5]

2-N

[6] Condition Number Estimates for Combined Potential Integral Operators in Acoustics and Their Boundary Element Discretisation [J].

Betcke, T. ;

Chandler-Wilde, S. N. ;

Graham, I. G. ;

Langdon, S. ;

Lindner, M. .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2011, 27 (01) :31-69

[7] ERROR ESTIMATES FOR THE ULTRA WEAK VARIATIONAL FORMULATION OF THE HELMHOLTZ EQUATION [J].

Buffa, Annalisa ;

Monk, Peter .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2008, 42 (06) :925-940

[8] Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem [J].

Cessenat, O ;

Despres, B .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (01) :255-299

[9]

DAUGE M, 1988, LECT NOTES MATH, V1341

[10]

Esterhazy S., 2011, LECT NOTES COMPUT SC, V83, P285

← 1 2 3 4 5 →