Towards discrete velte decompositions and narrow bounds for inf-sup constants

For the Velte decomposition of the function space into three orthogonal subspaces, the possibility of discrete equivalents is investigated and some first results are derived for conforming finite element methods. For the difference approximation on a staggered grid, a full description of the discrete Velte decomposition is given. In the continuous case, we consider the connection of the Velte decomposition to an orthogonal decomposition of the pressure space and to the inf-sup stability condition of the Stokes problem. Some bounds for inf-sup constants in the continuous two-dimensional case and numerous discrete inf-sup constants have been computed.