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In this paper we revisit the definition of the stabilization parameter in the finite element approximation of the convection–diffusion–reaction equation. The starting point is the decomposition of the unknown
into its finite element component and a subgrid scale that needs to be approximated. In order to incorporate the distortion of the mesh into this approximation, we transform the equation for the subgrid
scale within each element to the shape-regular reference domain. The expression for the subgrid scale arises from an approximate Fourier analysis and the identification of the wave number direction where
instabilities are most likely to occur. The final outcome is an expression for the stabilization parameter that accounts for anisotropy and the dominance of either convection or reaction terms in the equation.
CitationPrincipe, R.; Codina, R. On the stabilization parameter in the subgrid scale approximation of scalar convection-diffusion-reaction equations on distorted meshes. "Computer methods in applied mechanics and engineering", 01 Abril 2010, vol. 199, núm. 21-22, p. 1386-1402.
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