On some recent adventures into improved finite element CFD methods for convective transport (Q1267940)

The UTK (University of Tennessee, Knoxville) CFD research group describes its search on examining generalized Taylor series (Lax-Wendroff) methods, characteristic Euler flux resolutions, subgrid embedded high-degree Lagrange bases with static condensation, and assembled-stencil Fourier analysis optimization for finite element weak statement implementations. For appropriate model problems, including steady convection-diffusion and pure unsteady convection, and benchmark Navier-Stokes definitions, recent advances have led to accurate monotone methods with linear basis efficiency. This contribution highlights the theoretical developments, and presents quantitative documentation of achievable high quality solutions.