An anistropic functional setting for convection-diffusion problems (Q2763867)

Consistently stabilized discrete approximations for the convection-diffusion problems are investigated. The aim of the presented new functional framework is the evaluation of the residuals in an inner product of the type \(H^{1/2}\) and the realization of this inner product via explicitely computable decomposition of functional spaces.NEWLINENEWLINENEWLINEThe authors propose to improve this approach by taking into account the anisotropic nature of the convection-diffusion operator. Estimations for both the exact and discrete solutions, which are uniform with respect to the diffusion parameter, are developed. Some results concerning the convergence of the proposed approximations are also derived. A functional framework involving anisotropic Sobolev spaces, which depend on the velocity field is suggested.