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J. Melenk, S. Sauter:
"Convergence analysis for finite element discretizations of the Helmholtz equation. Part I: the full space problem";
in: "ASC Report 15/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-01-8.

A rigorous convergence theory for Galerkin methods for a model Helmholtz problem
in Rd, d 2 {1, 2, 3} is presented. General conditions on the approximation properties of
the approximation space are stated that ensure quasi-optimality of the method. As an
application of the general theory, a full error analysis of the classical hp-version of the
finite element method (hp-FEM) is presented where the dependence on the mesh width
h, the approximation order p, and the wave number k is given explicitly. In particular, it
is shown that quasi-optimality is obtained under the conditions that kh/p is sufficiently
small and the polynomial degree p is at least O(log k).

Helmholtz equation at high wave number, stability, convergence, hp-finite elements

http://www.asc.tuwien.ac.at/preprint/2008/asc15x2008.pdf