A multiscale/stabilized finite element method for the advection–diffusion equation

This paper presents a multiscale method that yields a stabilized finite element formulation for the advection–diffusion equation. The multiscale method arises from a decomposition of the scalar field into coarse (resolved) scale and fine (unresolved) scale. The resulting stabilized formulation possesses superior properties like that of the SUPG and the GLS methods. A significant feature of the present method is that the definition of the stabilization term appears naturally, and therefore the formulation is free of any user-designed or user-defined parameters. Another important ingredient is that since the method is residual based, it satisfies consistency ab initio. Based on the proposed formulation, a family of 2-D elements comprising 3 and 6 node triangles and 4 and 9 node quadrilaterals has been developed. Numerical results show the good performance of the method on uniform, skewed as well as composite meshes and confirm convergence at optimal rates. 2004 Elsevier B.V. All rights reserved.