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

Keywords

Advanced Numerical Methods for Scientific Computing
Geosciences/Protection of Land and Water Resources
Code:
28/2025
Title:
Discontinuous Galerkin time integration for second-order differential problems: formulations, analysis, and analogies
Date:
Saturday 10th May 2025
Author(s):
Ciaramella, G.; Gander, M.J.; Mazzieri, I.
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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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