On Runge-Kutta, collocation and discontinuous Galerkin methods: Mutual connections and resulting consequences to the analysis

Vlasák, Miloslav, and Roskovec, Filip. "On Runge-Kutta, collocation and discontinuous Galerkin methods: Mutual connections and resulting consequences to the analysis." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics AS CR, 2015. 231-236. <http://eudml.org/doc/269918>.

@inProceedings{Vlasák2015,
abstract = {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.},
author = {Vlasák, Miloslav, Roskovec, Filip},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {Runge-Kutta method; collocation method; discontinuous Galerkin method; stiff ordinary differential equation},
location = {Prague},
pages = {231-236},
publisher = {Institute of Mathematics AS CR},
title = {On Runge-Kutta, collocation and discontinuous Galerkin methods: Mutual connections and resulting consequences to the analysis},
url = {http://eudml.org/doc/269918},
year = {2015},
}

TY - CLSWK
AU - Vlasák, Miloslav
AU - Roskovec, Filip
TI - On Runge-Kutta, collocation and discontinuous Galerkin methods: Mutual connections and resulting consequences to the analysis
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2015
CY - Prague
PB - Institute of Mathematics AS CR
SP - 231
EP - 236
AB - 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.
KW - Runge-Kutta method; collocation method; discontinuous Galerkin method; stiff ordinary differential equation
UR - http://eudml.org/doc/269918
ER -