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Pré-Publication, Document De Travail Année : 2018

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).
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Dates et versions

hal-01902962 , version 1 (24-10-2018)
hal-01902962 , version 2 (11-11-2018)
hal-01902962 , version 3 (04-09-2019)
hal-01902962 , version 4 (09-09-2019)
hal-01902962 , version 5 (17-10-2019)

Identifiants

  • HAL Id : hal-01902962 , version 2

Citer

Simon Lemaire. Bridging the Hybrid High-Order and Virtual Element methods. 2018. ⟨hal-01902962v2⟩
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