hi everyone, I am dealing with a numerical method to solve the Helmholtz equation. As far as I know it is a second order elliptic PDE. I would like to know, if the Maximum Principle (aka Boundary Maximum Principle) holds for the Helmholtz eq., or where can I find explicit literature about it. In Collatz's 'Numerical Treatment of Differential Equations' it is written, that it is generally applicable to elliptic PDE-s in case of certain conditions. In other literature I read that it does not hold for the Helmholtz eq., because of it's special structure. The relevance of the question for me is the following: if one uses the solutions of the homogenous PDE as approximation functions for the numerical solution, the solution will satisfy the PDE, but not the boundary conditions. But in this case the error function will also satisfy the PDE, which if the Max. Principle is applicable, takes its maximum on the boundary, which is then good to have an upper bound on the error within the domain. thx, t.