A new stabilized finite element method for advection-diffusion-reaction equations using quadratic elements

A new stabilized FEM formulation for advective-diffusive-reactive problems is presented. The new method, called Spotted Petrov-Galekin (SPG), is a quadratic Petrov-Galerkin formulation based on two perturbations of the weight function: the first one is a generalized SUPG operator, the second one a nodal spot-like controlling operator for reactive instabilities. The formulation covers all the combinations of advective and reactive effects, associated to the dimensionless element Peclet and reaction numbers. After an introduction to the method, we present some numerical applications, addressing the reliability of SPG in turbomachinery CFD.