A review of discontinuous Galerkin time-stepping methods for wave propagation problems
Numerical Analysis
2025-05-12 v1 Numerical Analysis
Abstract
This chapter reviews and compares discontinuous Galerkin time-stepping methods for the numerical approximation of second-order ordinary differential equations, particularly those stemming from space finite element discretization of wave propagation problems. Two formulations, tailored for second- and first-order systems of ordinary differential equations, are discussed within a generalized framework, assessing their stability, accuracy, and computational efficiency. Theoretical results are supported by various illustrative examples that validate the findings, enhancing the understanding and applicability of these methods in practical scenarios.
Keywords
Cite
@article{arxiv.2505.05978,
title = {A review of discontinuous Galerkin time-stepping methods for wave propagation problems},
author = {Paola F. Antonietti and Alberto Artoni and Gabriele Ciaramella and Ilario Mazzieri},
journal= {arXiv preprint arXiv:2505.05978},
year = {2025}
}