Finite element wave model for Laplace equation

The mild-slope equation has been used for calculation of the surface gravity water wave transformation. Recently, its extended versions were introduced, which is capable of modeling wave transformation on rapidly varying topography. These equations were derived by integrating the Laplace equation vertically. Here, we develop a new finite element model to solve the Laplace equation directly while keeping the same computational efficiency as the mild-slope equation. This model assumes the vertical variation of the wave potential as a cosine hyperbolic function as done in the derivation of the mild-slope equation, and the Galerkin method is used to get a finite element solution. The computational domain is discretized with an infinite element. The applicability of the developed model is verified through example analyses of two-dimensional wave reflection and transmission.