Year: 2023
Author: Adem Kaya
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 1 : pp. 26–57
Abstract
An adapted-bubbles approach which is a modification of the residual-free bubbles (RFB) method, is proposed for the Helmholtz problem in 2D. A new two-level finite element method is introduced for the approximations of the bubble functions. Unlike the other equations such as the advection-diffusion equation, RFB method when applied to the Helmholtz equation, does not depend on another stabilized method to obtain approximations to the solutions of the sub-problems. Adapted-bubbles (AB) are obtained by a simple modification of the sub-problems. This modification increases the accuracy of the numerical solution impressively. We provide numerical experiments with the AB method up to $ch = 5$ where $c$ is the wavenumber and $h$ is the mesh size. Numerical tests show that the AB method is better by far than higher order methods available in the literature.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0083
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 1 : pp. 26–57
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Helmholtz equation adapted-bubbles residual-free bubbles two-level finite element.