Journal of Scientific Computing

, Volume 40, Issue 1–3, pp 257–272

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

Article

Abstract

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.

Keywords

Discontinuous Galerkin methods Finite element methods Wave equation Interior penalty method Leap-frog scheme 

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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

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