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Paola F Antonietti, Ilario Mazzieri, Niccolò Dal Santo, Alfio Quarteroni, A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics, IMA Journal of Numerical Analysis, Volume 38, Issue 4, October 2018, Pages 1709–1734, https://doi.org/10.1093/imanum/drx062
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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.