A low-order discontinuous Petrov-Galerkin method for the Stokes equations (Q1661651)

The authors propose a low-order discontinuous Petrov-Galerkin finite element method for the Stokes equations. The approach relies on piecewise constant and affine ansatz functions and piecewise affine and discontinuous lowest-order Raviart-Thomas test search functions. This low-order discretization for the Stokes equations allows for a direct proof of the discrete inf-sup condition with explicit constants. A priori and a posteriori error analysis of the method in the natural norms is provided along with several numerical experiments.