Journal of Scientific Computing

, Volume 40, Issue 1, pp 257–272

Optimal Error Estimates for the Fully Discrete Interior Penalty DG Method for the Wave Equation


DOI: 10.1007/s10915-008-9247-z

Cite this article as:
Grote, M.J. & Schötzau, D. J Sci Comput (2009) 40: 257. doi:10.1007/s10915-008-9247-z


In Grote et al. (SIAM J. Numer. Anal., 44:2408–2431, 2006) a symmetric interior penalty discontinuous Galerkin (DG) method was presented for the time-dependent wave equation. In particular, optimal a-priori error bounds in the energy norm and the L2-norm were derived for the semi-discrete formulation. Here the error analysis is extended to the fully discrete numerical scheme, when a centered second-order finite difference approximation (“leap-frog” scheme) is used for the time discretization. For sufficiently smooth solutions, the maximal error in the L2-norm error over a finite time interval converges optimally as O(hp+1t2), where p denotes the polynomial degree, h the mesh size, and Δt the time step.


Discontinuous Galerkin methodsFinite element methodsWave equationInterior penalty methodLeap-frog scheme

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BaselBaselSwitzerland
  2. 2.Mathematics DepartmentUniversity of British ColumbiaVancouverCanada