Nonconforming Galerkin methods for the Helmholtz equation

Nonconforming Galerkin methods for a Helmholtz-like problem arising in seis mology are discussed both for standard simplicial linear elements and for s everal new rectangular elements related to bilinear or trilinear elements. Optimal order error estimates in a broken energy norm are derived for all e lements and in L-2 for some of the elements when proper quadrature rules ar e applied to the absorbing boundary condition. Domain decomposition iterati ve procedures are introduced for the nonconforming methods, and their conve rgence at a predictable rate is established. (C) 2001 John Wiley & Sons, In c.