An eigenvalue problem for a system of finite difference equations approximating a linear water wave equation (Q1185119)

We give analytical representations of solutions of an eigenvalue problem for a system of finite difference equations approximating a linear water wave equation in a rectangular region. The eigenvalue problem is derived using the finite element method with the linear basis functions associated with the Friedrichs-Keller type triangulation, and with the generalized mass matrix \(\theta M+(1-\theta)\overline M\) on the water surface at rest, where \(M\), and \(\overline M\), are the consistent mass matrix, and the lumped mass matrix, respectively.