Gaussian quadrature rules and -stability of Galerkin schemes for ODE.
Bensebah, Ali, Dubeau, François, Gélinas, Jacques (2003)
International Journal of Mathematics and Mathematical Sciences
Similarity:
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
Similarity:
Stability of ALE space-time discontinuous Galerkin method
Vlasák, Miloslav, Balázsová, Monika, Feistauer, Miloslav
Similarity:
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
Similarity:
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
Similarity:
On D-stability and B-stability.
M. van Veldhuizen (1983)
Numerische Mathematik
Similarity:
A Note on B-Stability of Runge-Kutta Methods.
M.N. Spijker, W.H. Hundsdorfer (1980/81)
Numerische Mathematik
Similarity:
Stability of the method of lines.
Satish C. Reddy, Lloyd N. Trefethen (1992)
Numerische Mathematik
Similarity:
Time discretizations for evolution problems
Miloslav Vlasák (2017)
Applications of Mathematics
Similarity:
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.
Stability of Explicit Time Discretizations for Solving Initial Value Problems.
O. Nevanlinna, R. Jeltsch (1981)
Numerische Mathematik
Similarity:
Arbitrary high-order finite element schemes and high-order mass lumping
Sébastien Jund, Stéphanie Salmon (2007)
International Journal of Applied Mathematics and Computer Science
Similarity:
Computers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elementsof order k and show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit...