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

Cyril Agut, Julien Diaz & Abdelaâziz Ezziani

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

Published online: 2012-12

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  • Abstract

We present a new high order method in space and time for solving the wave equation, based on a new interpretation of the "Modified Equation" technique. Indeed, contrary to most of the works, we consider the time discretization before 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 Galerkin method for the discretization of this operator, and we provide numerical experiments proving that the new method is more accurate than the classical Modified Equation technique with a lower computational burden.

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@Article{CiCP-11-691, author = {}, title = {High-Order Schemes Combining the Modified Equation Approach and Discontinuous Galerkin Approximations for the Wave Equation}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {2}, pages = {691--708}, abstract = {

We present a new high order method in space and time for solving the wave equation, based on a new interpretation of the "Modified Equation" technique. Indeed, contrary to most of the works, we consider the time discretization before 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 Galerkin method for the discretization of this operator, and we provide numerical experiments proving that the new method is more accurate than the classical Modified Equation technique with a lower computational burden.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.311209.051110s}, url = {http://global-sci.org/intro/article_detail/cicp/7386.html} }
TY - JOUR T1 - High-Order Schemes Combining the Modified Equation Approach and Discontinuous Galerkin Approximations for the Wave Equation JO - Communications in Computational Physics VL - 2 SP - 691 EP - 708 PY - 2012 DA - 2012/12 SN - 11 DO - http://dor.org/10.4208/cicp.311209.051110s UR - https://global-sci.org/intro/article_detail/cicp/7386.html KW - AB -

We present a new high order method in space and time for solving the wave equation, based on a new interpretation of the "Modified Equation" technique. Indeed, contrary to most of the works, we consider the time discretization before 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 Galerkin method for the discretization of this operator, and we provide numerical experiments proving that the new method is more accurate than the classical Modified Equation technique with a lower computational burden.

Cyril Agut, Julien Diaz & Abdelaâziz Ezziani. (2020). High-Order Schemes Combining the Modified Equation Approach and Discontinuous Galerkin Approximations for the Wave Equation. Communications in Computational Physics. 11 (2). 691-708. doi:10.4208/cicp.311209.051110s
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