Gaussian quadrature rules and -stability of Galerkin schemes for ODE.
Bensebah, Ali, Dubeau, François, Gélinas, Jacques (2003)
International Journal of Mathematics and Mathematical Sciences
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Displaying similar documents to “Stability of ALE discontinuous Galerkin method with Radau quadrature”
Gaussian quadrature rules and -stability of Galerkin schemes for ODE.
Stability of the Lagrange-Galerkin method with non-exact integration
K. W. Morton, A. Priestley, E. Suli (1988)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Stability of ALE space-time discontinuous Galerkin method
Vlasák, Miloslav, Balázsová, Monika, Feistauer, Miloslav
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We assume the heat equation in a time dependent domain, where the evolution of the domain is described by a given mapping. The problem is discretized by the discontinuous Galerkin (DG) method in space as well as in time with the aid of Arbitrary Lagrangian-Eulerian (ALE) method. The sketch of the proof of the stability of the method is shown.
On Runge-Kutta, collocation and discontinuous Galerkin methods: Mutual connections and resulting consequences to the analysis
Vlasák, Miloslav, Roskovec, Filip
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Discontinuous Galerkin (DG) methods are starting to be a very popular solver for stiff ODEs. To be able to prove some more subtle properties of DG methods it can be shown that the DG method is equivalent to a specific collocation method which is in turn equivalent to an even more specific implicit Runge-Kutta (RK) method. These equivalences provide us with another interesting view on the DG method and enable us to employ well known techniques developed already for any of these methods....
Stability of Reducible Quadrature Methods for Volterra Integral Equations of the Second Kind.
Z. Jackiewicz, V.L. Bakke (1985)
Numerische Mathematik
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On D-stability and B-stability.
M. van Veldhuizen (1983)
Numerische Mathematik
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A Note on B-Stability of Runge-Kutta Methods.
M.N. Spijker, W.H. Hundsdorfer (1980/81)
Numerische Mathematik
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Stability of the method of lines.
Satish C. Reddy, Lloyd N. Trefethen (1992)
Numerische Mathematik
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Time discretizations for evolution problems
Miloslav Vlasák (2017)
Applications of Mathematics
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The aim of this work is to give an introductory survey on time discretizations for liner parabolic problems. The theory of stability for stiff ordinary differential equations is explained on this problem and applied to Runge-Kutta and multi-step discretizations. Moreover, a natural connection between Galerkin time discretizations and Runge-Kutta methods together with order reduction phenomenon is discussed.