Model problem

Our purpose in examining this test problem is to measure directly the effect of mesh refinement and the resulting mesh interfaces on a known wave that is sensitive to phase errors, while concurrently being able to visually display a meaningful picture of the effects of the refinement induced error on the solution. The refined mesh must be able to adequately capture the diffraction behavior, so that the plane wave front bends as it passes through the slit. Given that the coarse and refined meshes are sufficiently accurate, the phase errors introduced during the problem solution will be a function of th sound speed on the two grids plus the coarse/refined grid interaction errors.