@Article{NMTMA-16-1,
author = {Kaya, Adem},
title = {Application of Adapted-Bubbles to the Helmholtz Equation with Large Wavenumbers in 2D},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2023},
volume = {16},
number = {1},
pages = {26--57},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2022-0083},
url = {https://global-sci.com/article/90848/application-of-adapted-bubbles-to-the-helmholtz-equation-with-large-wavenumbers-in-2d}
}