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Article

Vlasák, Miloslav ; Roskovec, Filip
On Runge-Kutta, collocation and discontinuous Galerkin methods: Mutual connections and resulting consequences to the analysis. (English). In: Chleboun, J., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 8-13, 2014. Institute of Mathematics AS CR, Prague, 2015. pp. 231-236
MSC: 65L04, 65L05, 65L06, 65L60
Keywords:
Runge-Kutta method; collocation method; discontinuous Galerkin method; stiff ordinary differential equation
Summary:
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. Our aim will be proving the superconvergence property of the DG method in Radau quadrature nodes.
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