Bridging the Hybrid High-Order and Virtual Element methods

Simon Lemaire (1)

1 RAPSODI - Reliable numerical approximations of dissipative systems

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. This allows us to perform a unified study of conforming/nonconforming-Virtual Element/Hybrid High-Order methods, which happens to shed new light on the analysis of Virtual Element methods.

Domaines: Analyse numérique [math.NA]

Simon Lemaire. Bridging the Hybrid High-Order and Virtual Element methods. 2018. ⟨hal-01902962v1⟩