An adapted-bubbles approach which is a modification of the residualfree 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 ...An adapted-bubbles approach which is a modification of the residualfree 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.展开更多
文摘An adapted-bubbles approach which is a modification of the residualfree 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.
