TY - JOUR KW - Helmholtz equation KW - finite element method KW - coercive variational formulation KW - pollution effect KW - wavenumber-explicit analysis KW - GMRES AV - public JF - Journal of Computational and Applied Mathematics SN - 1879-1778 SP - 110 ID - discovery10071583 N2 - A new, coercive formulation of the Helmholtz equation was introduced in [1]. 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 k ? ?, 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. EP - 131 A1 - Diwan, GC A1 - Moiola, A A1 - Spence, EA UR - https://doi.org/10.1016/j.cam.2018.11.035 VL - 352 Y1 - 2019/05/15/ TI - Can coercive formulations lead to fast and accurate solution of the Helmholtz equation? PB - ELSEVIER SCIENCE BV N1 - This version is the author accepted manuscript. For information on re-use, please refer to the publisher?s terms and conditions. ER -