Discretization of the hydrostatic Stokes system by stabilized finite elements of equal order

This work addresses stabilized equal-order finite elements for the hydrostatic approximation of the three-dimensional (3D) Stokes equations which is also called 2.5D Stokes problem. By defining appropriate averaging operators, several stabilized schemes for the two-dimensional (2D) Stokes problem can be generalized to this 2.5D problem, as e.g. pressure stabilized Petrov-Galerkin, local projection, continuous interior penalty and Galerkin-Least-squares methods. However, it is not a priori clear if stability and a priori estimates of the 2D case carry over to the 2.5D case. In this work, we show stability and give a priori estimates under relative moderate assumptions on the three-dimensional grid. Numerical results support our theoretical results. Sección en el CEDYA 2011: Sesión Especial