A Combined Entropy and Output-based Adaptive Approach Using a Stabilized Continuous Finite Element Formulation

Adaptive mesh refinement driven by combining an error indicator derived from using an adjoint on a user-specified engineering scalar output and one derived directly from entropy variables has previously shown benefits in cost and accuracy for many applications. By leveraging indicators obtained from both approaches, the relative downsides of each approach can be limited. Numerous examples of both steady and unsteady simulations using a variety of governing equations highlight the possible benefits to both accuracy and cost that a combined error indicator approach can present. Previous works demonstrating this approach all relied on a discontinuous Galerkin (DG) discretization. In this work, the characteristics of the combined approach are demonstrated using a continuous finite element formulation, the streamline upwind/Petrov Galerkin (SUPG) method. Despite using a completely different discretization, similar advantages of the combined approach are demonstrated for simulations that use the steady-state inviscid Navier-Stokes equations. In addition, direct comparisons of error estimates and adaptive meshes are made for the various adaptive strategies using both SUPG and DG formulations.