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Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?


Babuska, I; Sauter, S (1997). Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers? SIAM Journal on Numerical Analysis, 34(6):2392-2423.

Abstract

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 approximation with increasing wave number. Many attempts have been presented in the literature to eliminate this lack of robustness by 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

Abstract

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 approximation with increasing wave number. Many attempts have been presented in the literature to eliminate this lack of robustness by 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

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1997
Deposited On:27 Feb 2010 02:12
Last Modified:05 Apr 2016 13:26
Publisher:Society for Industrial and Applied Mathematics
ISSN:0036-1429
Additional Information:©1997 Society for Industrial and Applied Mathematics
Publisher DOI:https://doi.org/10.1137/S0036142994269186

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