A uniformly stable family of mixed hp-finite elements with continuous pressures for incompressible flow

A new family of mixed hp-finite elements is presented for the discretization of planar Stokes flow on meshes of curvilinear, quadrilateral elements. The elements involve continuous pressures and are shown to be stable with an inf-sup constant bounded below independently of the mesh-size h and the spectral order p. The spaces have balanced approximation properties - the orders of approximation in h and p are equal for both the velocity and the pressure. This is the first example of a uniformly stable method with continuous pressures for spectral element discretization of Stokes equations, valid for geometrically refined meshes and curvilinear elements.