Polynomials in the Sobolev World
Résumé
This three chapter document addresses continuity and lifting of traces in singular domains, such as polygons and polyhedra. Compatibility conditions at corners and edges are described. Lifting operators are constructed on reference square and cube, with the following two requirements: 1. They should send polynomial on polyomials without increasing the partial degrees, 2. They should be stable in optimal Sobolev norms, standard and weighted. As a by-product, an important result about the interpolation between polynomial spaces P_N with different Sobolev norms is derived: Functional interpolation between 1. The space P_N provided with the Hm norm 2. The same space P_N provided with the L2 norm yields once more the space P_N with the right Sobolev norm Hs , and with equivalence constants independent of the degree N. Inverse inequalities are also investigated.
Domaines
Analyse numérique [math.NA]
Origine : Fichiers produits par l'(les) auteur(s)
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