, Volume 37, Issue 4, pp 207–232

An hp a priori error analysis of¶the DG time-stepping method for initial value problems

  • D. Schötzau
  • C. Schwab

DOI: 10.1007/s100920070002

Cite this article as:
Schötzau, D. & Schwab, C. CALCOLO (2000) 37: 207. doi:10.1007/s100920070002


The Discontinuous Galerkin (DG) time-stepping method for the numerical solution of initial value ODEs is analyzed in the context of the hp-version of the Galerkin method. New a priori error bounds explicit in the time steps and in the approximation orders are derived and it is proved that the DG method gives spectral and exponential accuracy for problems with smooth and analytic time dependence, respectively. It is further shown that temporal singularities can be resolved at exponential rates of convergence if geometrically refined time steps are employed.

Copyright information

© Springer-Verlag Italia 2000

Authors and Affiliations

  • D. Schötzau
    • 1
  • C. Schwab
    • 2
  1. 1.School of Mathematics, University of Minnesota, Vincent Hall, 206 Church Street SE, Minneapolis, MN 55455, USA¶e-mail: schoetza@math.umn.eduUS
  2. 2.Seminar für Angewandte Mathematik, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland¶e-mail: schwab@sam.math.ethz.chCH