A weak Galerkin finite element method for the Navier–Stokes equations

Abstract In this paper, we propose and analyze a weak Galerkin finite element method for the Navier–Stokes equations. The new formulation hinges upon the introduction of weak gradient, weak divergence and weak trilinear operators. Moreover, by choosing the matching finite element triples, this new method not only obtains stability and optimal error estimates but also has a lot of attractive computational features: general finite element partitions of arbitrary polygons or polyhedra with certain shape regularity and parameter free. Finally, several numerical experiments assess the convergence properties of the new method and show its computational advantages.