Bridging the Hybrid High-Order and Virtual Element methods

Simon Lemaire (1)

1 RAPSODI - Reliable numerical approximations of dissipative systems

We present a unifying viewpoint at Hybrid High-Order and Virtual Element methods on general polytopal meshes in dimension $2$ or $3$, both in terms of formulation and analysis. We focus on a model Poisson problem. To build our bridge, (i) we transcribe the (conforming) Virtual Element method into the Hybrid High-Order framework, and (ii) we prove $H^m$ approximation properties for the local polynomial projector in terms of which the local Virtual Element discrete bilinear form is defined. This allows us to perform a unified analysis of Virtual Element/Hybrid High-Order methods, that sheds new light on the similarities and differences between the conforming and nonconforming cases.

Domaines: Analyse numérique [math.NA]

Simon Lemaire. Bridging the Hybrid High-Order and Virtual Element methods. 2019. ⟨hal-01902962v3⟩