| 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. |
