In this paper, a class of cell centered finite volume schemes, on general unstructured meshes, for a linear convection-diffusion problem, is studied. The convection and the diffusion are respectively approximated by means of an upwind scheme and the so called diamond cell method [4]. Our main result is an error estimate of order h, assuming only the W 2,p (for p > 2) regularity of the continuous solution, on a mesh of quadrangles. The proof is based on an extension of the ideas developed in [12]. Some new difficulties arise here, due to the weak regularity of the solution, and the necessity to approximate the entire gradient, and not only its normal component, as in [12]. Résumé. Dans cet article, onétudie une classe de schémas volumes finis sur des maillages stucturés généraux, pour un problème linéaire de convection diffusion. La convection est approchée par un schéma décentré amont, et la diffusion par un schéma dit "des cellules diamants" [4]. On démontre une estimation d'erreur d'ordre h pour une solution continue dans W 2,p (p > 2), sur des maillages de quadrangles. La démonstration est une généralisation des idées de [12]. Les nouvelles difficultés sont la régularité plus faible de la solution exacte et la nécessité de construire une approximation du gradient et pas seulement de sa composante normale aux interfaces.

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Icephobic coatings for aircraft and other surfaces subjected to ice accretion have generated great interest in the past two decades, due to the advancement of nanomaterials, coating fabrication methods, biomimetics, and a more in-depth understanding of ice nucleation and ice adhesion. Icephobic coatings have demonstrated the ability to repel water droplets, delay ice nucleation and significantly reduce ice adhesion. Despite these ongoing research activities and promising results, the findings reported hereafter suggest that coatings alone cannot be used for aircraft anti-icing and de-icing operations; rather, they should be considered as a complementary option to either thermal or mechanical ice protection methods, for reducing power consumption and the ecological footprint of these active systems and for expediting ground de-icing operations. This paper will first review the state-of-the-art of icephobic coatings for various applications, including their performance and existing deficiencies. The second part of this paper focuses on aerospace anti-icing and de-icing requirements and the need for hybrid systems to provide a complete ice protection solution. Lastly, several urgent issues facing further development in the field are discussed.