On the performance of SOLD methods for convection-diffusion problems with interior layers

Numerical solutions of convection–diffusion equations obtained using the Streamline–Upwind Petrov–Galerkin (SUPG) stabilisation typically possess spurious oscillations at layers. Spurious Oscillations at Layers Diminishing (SOLD) methods aim to suppress or at least diminish these oscillations without smearing the layers extensively. In the recent review by John and Knobloch (2007), numerical studies at convection–diffusion problems with constant convection whose solutions have boundary layers led to a pre-selection of the best available SOLD methods with respect to the two goals stated above. The behaviour of these methods is studied in this paper for a convection–diffusion problem with a non-constant convection field whose solution possesses an interior layer.