A new MOX Report entitled “A review of discontinuous Galerkin time-stepping methods for wave propagation problems” by Antonietti P.F.; Artoni, A.; Ciaramella, G.; Mazzieri, I. has appeared in the MOX Report Collection.
Check it out here: https://www.mate.polimi.it/biblioteca/add/qmox/27-2025.pdf
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.
