  A new high order accurate semi-implicit space-time Discontinuous Galerkin
method on staggered grids, for the simulation of viscous incompressible flows
on two-dimensional domains is presented. The designed scheme is of the
Arbitrary Lagrangian Eulerian type, which is suitable to work on fixed as well
as on moving meshes. In our space-time formulation, by expressing the numerical
solution in terms of piecewise space-time polynomials, an arbitrary high order
of accuracy in time is achieved through a simple and efficient method of Picard
iterations. For the dual mesh, the basis functions consist in the union of
continuous piecewise polynomials on the two subtriangles within the
quadrilaterals: this allows the construction of a quadrature-free scheme,
resulting in a very efficient algorithm. Some numerical examples confirm that
the proposed method outperforms existing ones.
