A new, coercive formulation of the Helmholtz equation was introduced in
[Moiola, Spence, SIAM Rev. 2014]. In this paper we investigate h-version
Galerkin discretisations of this formulation, and the iterative solution of the
resulting linear systems. We find that the coercive formulation behaves
similarly to the standard formulation in terms of the pollution effect (i.e. to
maintain accuracy as kββ, h must decrease with k at the same rate
as for the standard formulation). We prove k-explicit bounds on the number of
GMRES iterations required to solve the linear system of the new formulation
when it is preconditioned with a prescribed symmetric positive-definite matrix.
Even though the number of iterations grows with k, these are the first such
rigorous bounds on the number of GMRES iterations for a preconditioned
formulation of the Helmholtz equation, where the preconditioner is a symmetric
positive-definite matrix.Comment: 27 pages, 7 figure