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Basic Principles of Hybrid High-Order Methods: The Poisson Problem

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The Hybrid High-Order Method for Polytopal Meshes

Part of the book series: MS&A ((MS&A,volume 19))

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Abstract

In this chapter we introduce the main ideas underlying HHO methods, using to this purpose the Poisson problem: Find \(u:\Omega \to \mathbb {R}\) such that

$$\displaystyle \begin{aligned} \begin{array}{rcl} -{\Delta} u &= f \qquad \text{in}\ \Omega, \\ u &= 0 \qquad \text{on}\ \partial\Omega, \end{array} \end{aligned}$$

where Ω is an open bounded polytopal subset of \(\mathbb {R}^n\), n ≥ 2, with boundary ∂ Ω and \(f:\Omega \to \mathbb {R}\) is a given volumetric source term, assumed to be in L 2( Ω).

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Authors and Affiliations

  1. Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, Montpellier, France

    Daniele Antonio Di Pietro

  2. School of Mathematics, Monash University, Clayton, VIC, Australia

    Jérôme Droniou

Authors
  1. Daniele Antonio Di Pietro
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  2. Jérôme Droniou
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Di Pietro, D.A., Droniou, J. (2020). Basic Principles of Hybrid High-Order Methods: The Poisson Problem. In: The Hybrid High-Order Method for Polytopal Meshes. MS&A, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-030-37203-3_2

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