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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A Hybrid High-Order method for Leray–Lions elliptic equations on general meshes
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by Daniele A. Di Pietro and Jérôme Droniou PDF
Math. Comp. 86 (2017), 2159-2191 Request permission


In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady nonlinear Leray–Lions problems. The proposed method has several assets, including the support for arbitrary approximation orders and general polytopal meshes. This is achieved by combining two key ingredients devised at the local level: a gradient reconstruction and a high-order stabilization term that generalizes the one originally introduced in the linear case. The convergence analysis is carried out using a compactness technique. Extending this technique to HHO methods has prompted us to develop a set of discrete functional analysis tools whose interest goes beyond the specific problem and method addressed in this work: (direct and) reverse Lebesgue and Sobolev embeddings for local polynomial spaces, $L^{p}$-stability and $W^{s,p}$-approximation properties for $L^{2}$-projectors on such spaces, and Sobolev embeddings for hybrid polynomial spaces. Numerical tests are presented to validate the theoretical results for the original method and variants thereof.
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Additional Information
  • Daniele A. Di Pietro
  • Affiliation: University of Montpellier, Institut Montpéllierain Alexander Grothendieck, 34095 Montpellier, France
  • Email:
  • Jérôme Droniou
  • Affiliation: School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia
  • MR Author ID: 655312
  • Email:
  • Received by editor(s): August 8, 2015
  • Received by editor(s) in revised form: March 23, 2016
  • Published electronically: December 21, 2016
  • Additional Notes: This work was partially supported by ANR project HHOMM (ANR-15-CE40-0005).
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 2159-2191
  • MSC (2010): Primary 65N08, 65N30, 65N12
  • DOI:
  • MathSciNet review: 3647954