Dual system least squares finite element method for the Helmholtz equation

This paper uses LL^∗ method to solve Helmholtz equation in case when the frequency parameter is large. The Helmholtz equation is reformulated to the first order system by introducing a new variable and then the corresponding dual problem is considered. The unique existence to the weak solution of the dual problem is proven and the explicit forms of continuity and coercivity constants depending on frequency parameter are developed. We describe numerical experiments with various scalings that result in different performances based on the a priori error estimation. The results are presented and compared with the ones that are obtained by the standard least-squares finite element approach.