Volume 11, Issue 2
High-order Schemes Combining the Modified Equation Approach and Discontinuous Galerkin Approximations for the Wave Equation

Cyril Agut ,  Julien Diaz and Abdelaâziz Ezziani

10.4208/cicp.311209.051110s

Commun. Comput. Phys., 11 (2012), pp. 691-708.

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  • Abstract

We present a new high order method in space and time for solving the wave equation, basedonanewinterpretationofthe“ModifiedEquation” technique. Indeed, contrary to most of the works, we consider the time discretizationbefore the space discretization. After the time discretization, an additional biharmonic operator appears, which can not be discretized by classical finite elements. We propose a new Discontinuous Galerkinmethod forthediscretizationof this operator,andweprovidenumerical experiments proving that the new method is more accurate than the classical Modified Equation technique with a lower computational burden. 

  • History

Published online: 2012-12

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