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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.
Thierry Gallouët +4 more
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SIAM Journal on Numerical Analysis, 1989
This article presents a new method of integrating evolution differential equations—the non-linear Galerkin method—that is well adapted to the long-term integration of such equations.While the usual Galerkin method can be interpreted as a projection of the considered equation on a linear space, the methods considered here are related to the projection ...
Roger Temam, Martine Marion
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This article presents a new method of integrating evolution differential equations—the non-linear Galerkin method—that is well adapted to the long-term integration of such equations.While the usual Galerkin method can be interpreted as a projection of the considered equation on a linear space, the methods considered here are related to the projection ...
Roger Temam, Martine Marion
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A Galerkin method for Stefan problems
Applied Mathematics and Computation, 1992The one-dimensional Stefan problem is transformed to a convection- diffusion problem on a fixed interval. This transformed problem is then solved by a Galerkin method based on piecewise-linear splines. The algorithm is tested on a standard example for which an analytic solution is known.
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2020
Before we can understand the nuances of the various methods for discretizing nonlinear partial differential equations in space, we must first realize the choices that we have at our disposal. We can categorize the possible methods as follows: 1. methods that use the differential form of the equations and 2.
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Before we can understand the nuances of the various methods for discretizing nonlinear partial differential equations in space, we must first realize the choices that we have at our disposal. We can categorize the possible methods as follows: 1. methods that use the differential form of the equations and 2.
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A Note on the Galerkin Method's Stability
Mathematische Nachrichten, 1995AbstractNumerical stability of the Galerkin method for some class of semilinear evolution equations is studied. The stability is established in thelp(1 <p < ∞) norms. Our results are applied to the special coordinate systems. All the conditions of the stability theorems proved in this note may be readily verifiable in practice for them.
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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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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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1984
Galerkin methods have been used to solve problems in structural mechanics, dynamics, fluid flow, hydrodynamic stability, magnetohydrodynamics, heat and mass transfer, acoustics, microwave theory, neutron transport, etc. Problems governed by ordinary differential equations, partial differential equations, and integral equations have been investigated ...
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Galerkin methods have been used to solve problems in structural mechanics, dynamics, fluid flow, hydrodynamic stability, magnetohydrodynamics, heat and mass transfer, acoustics, microwave theory, neutron transport, etc. Problems governed by ordinary differential equations, partial differential equations, and integral equations have been investigated ...
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2015
Chapter 11 considered spectral expansions of square-integrable random variables, random vectors and random fields of the form $$\displaystyle{U =\sum _{k\in \mathbb{N}_{0}}u_{k}\varPsi _{k},}$$ where \(U \in L^{2}(\varTheta,\mu;\mathcal{U})\), \(\mathcal{U}\) is a Hilbert space in which the corresponding deterministic variables/vectors/fields ...
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Chapter 11 considered spectral expansions of square-integrable random variables, random vectors and random fields of the form $$\displaystyle{U =\sum _{k\in \mathbb{N}_{0}}u_{k}\varPsi _{k},}$$ where \(U \in L^{2}(\varTheta,\mu;\mathcal{U})\), \(\mathcal{U}\) is a Hilbert space in which the corresponding deterministic variables/vectors/fields ...
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