A Lagrange-Galerkin hp -Finite Element Method for a 3D Nonhydrostatic Ocean Model

We introduce in this paper a Lagrange-Galerkin hp -finite element method to calculate the numerical solution of a nonhydrostatic ocean model. The Lagrange-Galerkin method yields a Stokes-like problem the solution of which is computed by a second-order rotational splitting scheme that separates the calculation of the velocity and pressure, the latter is decomposed into hydrostatic and nonhydrostatic components. We have tested the method in flows where the nonhydrostatic effects are important. The results are very encouraging.