Adaptive BEM with optimal convergence rates for the Helmholtz equation
Adaptive BEM with optimal convergence rates for the Helmholtz equation
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DOI：
10.1016/j.cma.2018.12.006
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发表时间：
2019-04-01
影响因子：
7.2
通讯作者：
Praetorius, Dirk
中科院分区：
文献类型：
--
作者：
Bespalov, Alex;Betcke, Timo;Praetorius, Dirk
分析了二维和三维Helmholtz问题的弱奇异超奇异积分方程解的自适应边界元方法。所提出的自适应算法是由残差估计器引导的，不依赖于任何先验信息，即底层网格足够精细。我们证明了误差估计器在最优代数率下的收敛，与(粗)初始网格无关。作为技术贡献，我们证明了与Helmholtz方程相关的边界积分算子的某些局部逆型估计。(C)2018爱思唯尔B.V.保留所有权利。
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.