Abstract
In the previous chapters we have considered fully discrete schemes for the heat equation which were derived by first discretizing in the space variables by means of a Galerkin finite element method, which results in a system of ordinary differential equations with respect to time, and then applying a finite difference type time stepping method to this system to define a fully discrete solution. In this chapter, we shall apply the Galerkin method also in the time variable and thus define and analyze a method which treats the time and space variables similarly. The approximate solution will be sought as a piecewise polynomial function in t of degree at most q – 1, which is not necessarily continuous at the nodes of the defining partition.
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© 1997 Springer-Verlag Berlin Heidelberg
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Thomée, V. (1997). The Discontinuous Galerkin Time Stepping Method. In: Galerkin Finite Element Methods for Parabolic Problems. Springer Series in Computational Mathematics, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03359-3_12
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DOI: https://doi.org/10.1007/978-3-662-03359-3_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-03361-6
Online ISBN: 978-3-662-03359-3
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