A fully discrete Calderon Calculus for two dimensional time harmonic waves

In this paper, we present a fully discretized Calderon Calculus for the two dimensional Helmholtz equation. This full discretization can be understood as highly non-conforming Petrov-Galerkin methods, based on two staggered grids of mesh size h, Dirac delta distri- butions substituting acoustic charge densities and piecewise constant functions for approxi- mating acoustic dipole densities. The resulting numerical schemes from this calculus are all of order h 2 provided that the continuous equations are well posed. We finish by presenting some numerical experiments illustrating the performance of this discrete calculus.