Hierarchical basis for stabilized nite elementmethods for compressible owsChristian

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 nite element methods, as a means to attain this accuracy in the most cost eeective manner. Stabilized nite element methods (e.g. SUPG) have been proven to attain optimal rates of convergence for any polynomial order basis as well as perform well on a variety of ows including turbulence applications. We present a stabilized nite element formulation for uid 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.