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Les méthodes de Galerkine discontinues (mé … Les méthodes de Galerkine discontinues (méthodes GD, en abrégé) sont une classe de méthode numérique de résolution des équations aux dérivées partielles, nommées en référence au mathématicien Boris Galerkine. Elle réunit des propriétés de la méthode des éléments finis (approximation polynomiale de la solution par cellule) et de la méthode des volumes finis (définition locale de l'approximation et calcul des flux aux interfaces des cellules du maillage). Cette définition lui permet d'être appliquée à des systèmes d'équations hyperboliques, elliptiques et paraboliques, plus particulièrement aux problèmes dont le terme de premier ordre est dominant (équations de transport, électrodynamique, mécanique des fluides et physique des plasmas). Un des apports de la méthode de Galerkine discontinue, est de ne pas imposer la continuité de la solution numérique à l'interface entre un élément et son voisin. Cette caractéristique permet un découplage des éléments : « on raisonne localement », en se préoccupant moins des éléments voisins. Ceci permet de paralléliser le calcul et de réduire ainsi le temps de traitement.t de réduire ainsi le temps de traitement.
, In applied mathematics, discontinuous Gale … In applied mathematics, discontinuous Galerkin methods (DG methods) form a class of numerical methods for solving differential equations. They combine features of the finite element and the finite volume framework and have been successfully applied to hyperbolic, elliptic, parabolic and mixed form problems arising from a wide range of applications. DG methods have in particular received considerable interest for problems with a dominant first-order part, e.g. in electrodynamics, fluid mechanics and plasma physics. Discontinuous Galerkin methods were first proposed and analyzed in the early 1970s as a technique to numerically solve partial differential equations. In 1973 Reed and Hill introduced a DG method to solve the hyperbolic neutron transport equation. The origin of the DG method for elliptic problems cannot be traced back to a single publication as features such as jump penalization in the modern sense were developed gradually. However, among the early influential contributors were Babuška, J.-L. Lions, Joachim Nitsche and Miloš Zlámal. DG methods for elliptic problems were already developed in a paper by Garth Baker in the setting of 4th order equations in 1977. A more complete account of the historical development and an introduction to DG methods for elliptic problems is given in a publication by Arnold, Brezzi, Cockburn and Marini. A number of research directions and challenges on DG methods are collected in the proceedings volume edited by Cockburn, Karniadakis and Shu.e edited by Cockburn, Karniadakis and Shu.
, Разрывный метод Галёркина (англ. discontin … Разрывный метод Галёркина (англ. discontinuous Galerkin method, сокращенно DGM) — метод решения операторных уравнений, в основном дифференциальных уравнений. Является развитием классического метода конечных элементов (МКЭ), основанного на вариационной постановке Галёркина.ного на вариационной постановке Галёркина.
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In applied mathematics, discontinuous Gale … In applied mathematics, discontinuous Galerkin methods (DG methods) form a class of numerical methods for solving differential equations. They combine features of the finite element and the finite volume framework and have been successfully applied to hyperbolic, elliptic, parabolic and mixed form problems arising from a wide range of applications. DG methods have in particular received considerable interest for problems with a dominant first-order part, e.g. in electrodynamics, fluid mechanics and plasma physics.amics, fluid mechanics and plasma physics.
, Разрывный метод Галёркина (англ. discontin … Разрывный метод Галёркина (англ. discontinuous Galerkin method, сокращенно DGM) — метод решения операторных уравнений, в основном дифференциальных уравнений. Является развитием классического метода конечных элементов (МКЭ), основанного на вариационной постановке Галёркина.ного на вариационной постановке Галёркина.
, Les méthodes de Galerkine discontinues (mé … Les méthodes de Galerkine discontinues (méthodes GD, en abrégé) sont une classe de méthode numérique de résolution des équations aux dérivées partielles, nommées en référence au mathématicien Boris Galerkine. Elle réunit des propriétés de la méthode des éléments finis (approximation polynomiale de la solution par cellule) et de la méthode des volumes finis (définition locale de l'approximation et calcul des flux aux interfaces des cellules du maillage). Cette définition lui permet d'être appliquée à des systèmes d'équations hyperboliques, elliptiques et paraboliques, plus particulièrement aux problèmes dont le terme de premier ordre est dominant (équations de transport, électrodynamique, mécanique des fluides et physique des plasmas).ique des fluides et physique des plasmas).
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Méthode de Galerkine discontinue
, Разрывный метод Галёркина
, Discontinuous Galerkin method
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