Hierarchical basis for stabilized finite element methods for compressible flows Original Research Article

The quest for more accurate numerical simulations of the Navier–Stokes equations has motivated the study of high-order piecewise-polynomial basis functions, also known as k-version finite element methods, as a means to attain this accuracy in the most cost effective manner. Stabilized finite element methods (e.g. streamline upwind Petrov Galerkin) have been proven to attain optimal rates of convergence for any polynomial order basis as well as perform well on a variety of flows including turbulence applications. We present a stabilized finite element formulation for fluid dynamics using mesh-entity based hierarchical basis functions. The implementation is shown to attain theoretical convergence results for the linear model problem as well as the Navier–Stokes equations.