Métodos de elementos finitos mistos híbridos estabilizados para escoamentos incompressíveis

Abstract

In this work, stabilized mixed hybrid finite element methods are proposed for the numerical simulation of incompressible flows, based on the models described by the Stokes, Oseen and Navier-Stokes equations. From a developed and analyzed formulation for the Stokes flow, we propose an extension for the Oseen and Navier-Stokes problems. The methods in question are characterized by the introduction of multipliers, defined as velocity and pressure traces, in order to weakly imposes the continuity between the elements. Due to the choice of multipliers, this strategy allows the elimination of variables, velocity and pressure, at the element level, condensing this information into the Lagrange multipliers defined at the edges of the elements, giving rise to a global problem that depends only the degrees of freedom of the multipliers. Once the multipliers have been determined, local problems can be solved at the element level. In this context, numerical studies are performed to evaluate the convergence rates in the L2-norm to each problem.