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The Discontinuous Galerkin Time Stepping Method

  • Vidar Thomée
Chapter
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 25)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Vidar Thomée
    • 1
  1. 1.Department of MathematicsChalmers University of TechnologyGöteborgSweden

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