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Discontinuous Galerkin Methods
2012In this final chapter we present the discontinuous Galerkin (dG) method. This method is based on finite element spaces that consist of discontinuous piecewise polynomials defined on a partition of the computational domain. Such methods are very flexible, for example, since they allow construction of more general methods and since they allow for simple ...
Mats G. Larson, Fredrik Bengzon
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Discontinuous Galerkin Methods
2018Two GDMs are obtained from the Discontinuous Galerkin setting. The first one recovers the high order SIPG schemes in the case of linear problems, the second one, based on average jumps, leads to simpler computations.
Jérôme Droniou +4 more
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Discontinuous Galerkin Methods
2016This chapter is devoted to the construction, based on discrete energy control, of discontinuous Galerkin methods (DGM) which are well-adapted to the solution of wave problems. In a first part, these methods are described by using an abstract framework for first-order linear hyperbolic problems which covers, in particular, all the transient wave ...
Gary Cohen, Sébastien Pernet
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1995
In den vorherigen Kapiteln wurde beschrieben, wie die FEM fur die Losung von Minimierungsproblemen und damit zusammenhangenden DG benutzt wird. Fur eine grose Anzahl von DG existiert jedoch kein aquivalentes Mini-mierungsproblem, so das auf sie die Ritzsche Methode nicht anwendbar ist.
J. J. I. M. van Kan, A. Segal
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In den vorherigen Kapiteln wurde beschrieben, wie die FEM fur die Losung von Minimierungsproblemen und damit zusammenhangenden DG benutzt wird. Fur eine grose Anzahl von DG existiert jedoch kein aquivalentes Mini-mierungsproblem, so das auf sie die Ritzsche Methode nicht anwendbar ist.
J. J. I. M. van Kan, A. Segal
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1977
Consider a separable Hilbert space H and a set M of its elements which is dense in H. According to Theorem 6.18, p. 79, if for some element u ∈ H $$\left( {u,v} \right) = 0\,\,\,holds\,for\,every\,\,\,v \in M,$$ (14.1) then it follows that u = 0 in H. Let now $${\varphi _1},{\varphi _2},\,...$$ (14.2) be a base in H. The assertion is
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Consider a separable Hilbert space H and a set M of its elements which is dense in H. According to Theorem 6.18, p. 79, if for some element u ∈ H $$\left( {u,v} \right) = 0\,\,\,holds\,for\,every\,\,\,v \in M,$$ (14.1) then it follows that u = 0 in H. Let now $${\varphi _1},{\varphi _2},\,...$$ (14.2) be a base in H. The assertion is
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2008
Die Formulierung des Randwert problems aus Kapitel 2 als Variationsproblem war muhsam, das Prinzip der Diskretisierung des Variationsproblems ist nun aber kurz darstellbar und lasst sich sehr allgemein formulieren.
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Die Formulierung des Randwert problems aus Kapitel 2 als Variationsproblem war muhsam, das Prinzip der Diskretisierung des Variationsproblems ist nun aber kurz darstellbar und lasst sich sehr allgemein formulieren.
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2002
In this chapter we consider an FK2 of the form (1.2.2): ϕ(x) — λ ∫ a b k(x,s)ϕ(s)ds = f (s), where a ≤ x,s ≤ b, and the kernel k(x,s) has a weak singularity at an endpoint. In numerical approximations, whether in quadrature, finite differences,finite elements, and the like, the computational methods generally use polynomials as basis functions to ...
Prem K. Kythe, Pratap Puri
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In this chapter we consider an FK2 of the form (1.2.2): ϕ(x) — λ ∫ a b k(x,s)ϕ(s)ds = f (s), where a ≤ x,s ≤ b, and the kernel k(x,s) has a weak singularity at an endpoint. In numerical approximations, whether in quadrature, finite differences,finite elements, and the like, the computational methods generally use polynomials as basis functions to ...
Prem K. Kythe, Pratap Puri
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1984
When evaluated on a uniform grid, the Galerkin method produces symmetric formulae. Thus odd-order derivatives lead to zero coefficients associated with the node at which the function is centered. The steady, two-dimensional convection-diffusion equation is $$ u\frac{\partial T}{\partial x}~+~v\frac{\partial T}{\partial y}~-~D\left( \frac{{{\partial
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When evaluated on a uniform grid, the Galerkin method produces symmetric formulae. Thus odd-order derivatives lead to zero coefficients associated with the node at which the function is centered. The steady, two-dimensional convection-diffusion equation is $$ u\frac{\partial T}{\partial x}~+~v\frac{\partial T}{\partial y}~-~D\left( \frac{{{\partial
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A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering, 2006
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