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arXiv · 2505.05985

Discontinuous Galerkin time integration for second-order differential problems: formulations, analysis, and analogies

Gabriele Ciaramella·Martin J. Gander·Ilario Mazzieri
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Abstract

We thoroughly investigate Discontinuous Galerkin (DG) discretizations as time integrators for second-order oscillatory systems, considering both second-order and first-order formulations of the original problem. Key contributions include new convergence analyses for the second-order formulation and equivalence proofs between DG and classical time-stepping schemes (such as Newmark schemes and general linear methods). In addition, the chapter provides a detailed review and convergence analysis for the first-order formulation, alongside comparisons of the proposed schemes in terms of accuracy, consistency, and computational cost.

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Gabriele Ciaramella, Martin J. Gander, Ilario Mazzieri. 2025-05-09. Discontinuous Galerkin time integration for second-order differential problems: formulations, analysis, and analogies. https://arxiv.org/abs/2505.05985

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