Importance of parameter optimization in a nonlinear stabilized method adding a crosswind diffusion

Abstract Numerical solutions of convection-dominated problems are known to exhibit spurious oscillations whose suppression requires the use of numerical stabilization. Stabilized methods which involve heuristic parameters are often applied. The parameters influence the quality of the solution but their optimal values are unknown. In this paper, we consider a stabilization method which adds numerical diffusion adaptively, based on minimizing a functional. The novelty of our approach consists in combining an error indicator with reduced residuals with a nonlinear SOLD method adding artificial diffusion in the crosswind direction. We demonstrate that this approach can lead to more physically meaningful solutions than techniques considered before.