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This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics. Hybrid High-Order methods are new-generation numerical methods for partial differential equations with features that set them apart from traditional ones. These include: the support of polytopal meshes, including non-star-shaped elements and hanging nodes; the possibility of having arbitrary approximation orders in any space dimension; an enhanced compliance with the physics; and a reduced computational cost thanks to compact stencil and static condensation. The first part of the monograph lays the foundations of the method, considering linear scalar second-order models, including scalar diffusion – possibly heterogeneous and anisotropic – and diffusion-advection-reaction. The second part addresses applications to more complex models from the engineering sciences: non-linear Leray-Lions problems, elasticity, and incompressible fluid flows. This book is primarily intended for graduate students and researchers in applied mathematics and numerical analysis, who will find here valuable analysis tools of general scope.

Computer mathematics. --- Mathematical physics. --- Applied mathematics. --- Engineering mathematics. --- Computational Mathematics and Numerical Analysis. --- Mathematical Applications in the Physical Sciences. --- Mathematical and Computational Engineering. --- Numerical analysis. --- Mathematical analysis --- Physical mathematics --- Physics --- Computer mathematics --- Electronic data processing --- Mathematics --- Engineering --- Engineering analysis

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This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields. Numerical analysis applied to the approximate solution of PDEs is a key discipline in applied mathematics, and over the last few years, several new paradigms have appeared, leading to entire new families of discretization methods and solution algorithms. This book is intended for researchers in the field.

Differential equations, Partial --- Asymptotic theory in partial differential equations --- Asymptotic expansions --- Asymptotic theory. --- Numerical analysis. --- Differential equations, partial. --- Computer science. --- Numerical Analysis. --- Partial Differential Equations. --- Computational Science and Engineering. --- Informatics --- Science --- Partial differential equations --- Mathematical analysis --- Partial differential equations. --- Computer mathematics. --- Computer mathematics --- Electronic data processing --- Mathematics

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Polyhedral functions. --- Discretization (Mathematics) --- Earth sciences --- Mathematics. --- Geosciences --- Environmental sciences --- Physical sciences --- Differential equations --- Functions, Polyhedral --- Modular functions --- Numerical solutions --- Ciències de la Terra --- Matemàtica --- Matemàtiques (Ciència) --- Ciència --- Alfabetisme matemàtic --- Àlgebra --- Anàlisi matemàtica --- Aritmètica --- Axiomes --- Biomatemàtica --- Congruències (Geometria) --- Congruències i residus --- Constants matemàtiques --- Descomposició (Matemàtica) --- Dinàmica --- Estadística --- Factorització (Matemàtica) --- Filtres (Matemàtica) --- Formes (Matemàtica) --- Formes normals (Matemàtica) --- Geometria --- Geografia matemàtica --- Inducció (Matemàtica) --- Infinit --- Lògica matemàtica --- Matemàtica aplicada --- Matemàtica japonesa --- Màxims i mínims --- Nombres --- Quarta dimensió --- Successions (Matemàtica) --- Teoria de conjunts --- Teoria de l'índex (Matemàtica) --- Teoria de la computació --- Variables (Matemàtica) --- Didàctica de la matemàtica --- Ensenyament de la matemàtica --- Història de la matemàtica --- Matemàtics --- Geociències --- Ciències ambientals --- Ciències del mar --- Edafologia --- Geobiologia --- Geofísica --- Geografia --- Geologia --- Geomàtica --- Geoquímica --- Hidrologia --- Meteorologia --- Ciències naturals

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This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics. Hybrid High-Order methods are new-generation numerical methods for partial differential equations with features that set them apart from traditional ones. These include: the support of polytopal meshes, including non-star-shaped elements and hanging nodes; the possibility of having arbitrary approximation orders in any space dimension; an enhanced compliance with the physics; and a reduced computational cost thanks to compact stencil and static condensation. The first part of the monograph lays the foundations of the method, considering linear scalar second-order models, including scalar diffusion – possibly heterogeneous and anisotropic – and diffusion-advection-reaction. The second part addresses applications to more complex models from the engineering sciences: non-linear Leray-Lions problems, elasticity, and incompressible fluid flows. This book is primarily intended for graduate students and researchers in applied mathematics and numerical analysis, who will find here valuable analysis tools of general scope.

Mathematics --- Mathematical physics --- Applied physical engineering --- Computer. Automation --- toegepaste wiskunde --- computers --- economie --- wiskunde --- fysica

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Mathematics --- Mathematical physics --- Applied physical engineering --- Computer. Automation --- toegepaste wiskunde --- computers --- economie --- wiskunde --- fysica