A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics

Abstract The aim of this work is to propose and analyse a new high-order discontinuous Galerkin finite element method for the time integration of a Cauchy problem for second-order ordinary differential equations. These equations typically arise after space semidiscretization of second-order hyperbol...

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Bibliographic Details
Published in:IMA journal of numerical analysis 2018-10, Vol.38 (4), p.1709-1734
Main Authors: Antonietti, Paola F, Mazzieri, Ilario, Dal Santo, Niccolò, Quarteroni, Alfio
Format: Article
Language:English
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Summary:Abstract The aim of this work is to propose and analyse a new high-order discontinuous Galerkin finite element method for the time integration of a Cauchy problem for second-order ordinary differential equations. These equations typically arise after space semidiscretization of second-order hyperbolic-type differential problems, e.g., wave, elastodynamics and acoustics equations. After introducing the new method, we analyse its well-posedness and prove a priori error estimates in a suitable (mesh-dependent) norm. Numerical results are also presented to verify our theoretical estimates.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/drx062