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The proposed method is valid in arbitrary space dimension and for fairly general polytopal meshes. Variable approximation degrees are also supported. We prove<jats:italic>hp<\/jats:italic>-convergence estimates for both the energy- and<jats:inline-formula id=\"j_cmam-2017-0009_ineq_9999_w2aab3b7e1179b1b6b1aab1c14b1b7Aa\"><jats:alternatives><m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><m:msup><m:mi>L<\/m:mi><m:mn>2<\/m:mn><\/m:msup><\/m:math><jats:tex-math>L^{2}<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-norms of the error, which are the first of this kind for Hybrid High-Order methods. These results hinge on a novel<jats:italic>hp<\/jats:italic>-approximation lemma valid for general polytopal elements in arbitrary space dimension. The estimates are additionally fully robust with respect to the heterogeneity of the diffusion coefficient, and show only a mild dependence on the square root of the local anisotropy, improving previous results for HHO methods. The expected exponential convergence behavior is numerically demonstrated on a variety of meshes for both isotropic and strongly anisotropic diffusion problems.<\/jats:p>","DOI":"10.1515\/cmam-2017-0009","type":"journal-article","created":{"date-parts":[[2017,6,20]],"date-time":"2017-06-20T10:01:30Z","timestamp":1497952890000},"page":"359-376","source":"Crossref","is-referenced-by-count":10,"title":["An<i>hp<\/i>-Hybrid High-Order Method for Variable Diffusion on General Meshes"],"prefix":"10.1515","volume":"17","author":[{"given":"Joubine","family":"Aghili","sequence":"first","affiliation":[{"name":"Institut Montpelli\u00e9rain Alexander Grothendieck , Universit\u00e9 de Montpellier , 34090 Montpellier , France"}]},{"given":"Daniele A.","family":"Di Pietro","sequence":"additional","affiliation":[{"name":"Institut Montpelli\u00e9rain Alexander Grothendieck , Universit\u00e9 de Montpellier , 34090 Montpellier , France"}]},{"given":"Berardo","family":"Ruffini","sequence":"additional","affiliation":[{"name":"Institut Montpelli\u00e9rain Alexander Grothendieck , Universit\u00e9 de Montpellier , 34090 Montpellier , France"}]}],"member":"374","published-online":{"date-parts":[[2017,6,17]]},"reference":[{"key":"2023033114491565422_j_cmam-2017-0009_ref_001_w2aab3b7e1179b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"J. 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