Bridging the Hybrid High-Order and Virtual Element methods
Résumé
We build a bridge between the Hybrid High-Order and the Virtual Element methods on general polytopal meshes in dimension 2 or 3, in the setting of a model Poisson problem. To do so, we reformulate the conforming-Virtual Element method as a (newborn) conforming-Hybrid High-Order method, and we derive $H^s$-approximation properties for the associated local polynomial projector (on which hinges the local discrete bilinear form). This allows us to perform a unified study of conforming/nonconforming-Virtual Element/Hybrid High-Order methods, which simplifies the classical error analysis of Virtual Element methods in broken $H^1$-seminorm, and sheds new light on the differences between the conforming and nonconforming cases (in particular in terms of mesh assumptions).
Domaines
Analyse numérique [math.NA]Origine | Fichiers produits par l'(les) auteur(s) |
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