Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?
Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?
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DOI：
10.1137/s0036142994269186
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发表时间：
1997-12-01
影响因子：
2.9
通讯作者：
Sauter, SA
中科院分区：
文献类型：
--
作者：
Babuska, IM;Sauter, SA
Helmholtz方程对波数具有鲁棒性，求解该方程的数值方法的发展是一个生动的研究课题。结果表明，随着波数的增加，伽辽金有限元法（FEM）的解与最佳近似解有很大的不同。在文献中已经提出了许多尝试，以消除这种缺乏鲁棒性的qv经典Galerkin FEM的各种修改。然而，我们将证明，在两个或更多的空间维度中，不可能消除这种所谓的污染效应。此外，我们将提出一个广义有限元在一维的行为鲁棒相对于波数。
The development of numerical methods for solving the Helmholtz equation, which behaves robustly with respect to the wave number, is a topic of vivid research. It was observed that the solution of the Galerkin finite element method (FEM) differs significantly from the best appl approximation with increasing wave number. Many attempts have been presented in the literature to eliminate this lack of robustness qv various modifications of the classical Galerkin FEM.However, we will prove that, in two and more space dimensions, it is impossible to eliminate this so-called pollution effect., Furthermore, we will present a generalized FEM in one dimension which behaves robustly with respect to the wave number.