Quasisolenoidal velocity-pressure finite element methods for the three-dimensional Stokes problem (Q1065524)

The three-dimensional Stokes problem with quasi-solenoidal velocity field is considered. First, a weak formulation to this problem is given, followed by existence and uniqueness results for the finite element solution, in the particular case of a parallepipedal domain. Convergence results (sufficient conditions) are obtained with reference to the used finite element method, that allows a sequence of velocity and pressure field converging with order one to the exact (weak) solution of the ``continuous'' problem. The work ends with corresponding numerical results of a given movement in the unit cube.