Adaptive BEM with optimal convergence rates for the Helmholtz equation

被引：13

作者：

Bespalov, Alex ^{[1
]}

Betcke, Timo ^{[2
]}

Haberl, Alexander ^{[3
]}

Praetorius, Dirk ^{[3
]}

机构：

[1] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England

[2] UCL, Ctr Inverse Problems, Gower St, London WC1E 6BT, England

[3] TU Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2019年 / 346卷

基金：

英国工程与自然科学研究理事会; 奥地利科学基金会;

关键词：

Boundary element method; Helmholtz equation; A posteriori error estimate; Adaptive algorithm; Convergence; Optimality; BOUNDARY-ELEMENT METHODS; POSTERIORI ERROR ESTIMATE; INTEGRAL-EQUATIONS; SCATTERING; EFFICIENCY; ALGORITHM; SURFACES; FEM;

D O I：

10.1016/j.cma.2018.12.006

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on any a priori information that the underlying meshes are sufficiently fine. We prove convergence of the error estimator with optimal algebraic rates, independently of the (coarse) initial mesh. As a technical contribution, we prove certain local inverse-type estimates for the boundary integral operators associated with the Helmholtz equation. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：260 / 287

页数：28

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