Discontinuous Galerkin time integration for second-order differential problems: formulations, analysis, and analogies
Numerical Analysis
2025-05-12 v1 Numerical Analysis
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.
Cite
@article{arxiv.2505.05985,
title = {Discontinuous Galerkin time integration for second-order differential problems: formulations, analysis, and analogies},
author = {Gabriele Ciaramella and Martin J. Gander and Ilario Mazzieri},
journal= {arXiv preprint arXiv:2505.05985},
year = {2025}
}