SUMMARYThe unsteady compressible flow equations are solved using a stabilized finiteâelement formulation with C0 elements. In 2D, the performance of threeânoded linear and sixânoded quadratic triangular elements is compared. In 3D, the relative performance is evaluated for 6ânoded linear and 18ânoded quadratic wedge elements. Results are compared for the solutions to Euler, laminar, and turbulent flows at different Mach numbers for several flow problems. The finiteâelement meshes considered for comparison have same location of nodes for the linear and quadratic interpolations. For the turbulent flow, the SpalartâAllmaras model is used for closure. It is found that the quadratic elements yield better performance than the linear elements. This is attributed to accurate representation of the stabilization terms that involve secondâorder derivatives in the formulation. When these terms are dropped from the formulation with quadratic interpolation, the numerical results are similar to those obtained with linear interpolation. The absence of these terms result in added numerical diffusion that seems to give the effect of a relatively reduced Reynolds number. For the same location of nodes, the computations with the linear triangular and wedge elements are approximately 20% and 100% faster than those with quadratic triangular and wedge elements, respectively. However, if the same quadrature rule for numerical integration is used for both interpolations, the computations with quadratic elements are approximately 20% and 45% faster in 2D and 3D, respectively. Copyright Š 2014 John Wiley & Sons, Ltd.