A review of discontinuous Galerkin time-stepping methods for wave propagation problems

TL;DR

This paper reviews and compares discontinuous Galerkin time-stepping methods for wave propagation problems, focusing on stability, accuracy, and efficiency through theoretical analysis and illustrative examples.

Contribution

It provides a comprehensive comparison of formulations for second- and first-order systems, advancing understanding of their practical stability and accuracy.

Findings

Discontinuous Galerkin methods are effective for wave propagation.

Theoretical analysis confirms stability and accuracy.

Numerical examples validate the methods' practical applicability.

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.