An energy-based discontinuous Galerkin method for the wave equation with nonsmooth solutions
Numerical Analysis
2025-07-03 v1 Numerical Analysis
Abstract
We develop a stable and high-order accurate discontinuous Galerkin method for the second order wave equation, specifically designed to handle nonsmooth solutions. Our approach integrates the energy-based discontinuous Galerkin method with the oscillation-free technique to effectively suppress spurious oscillations near solution discontinuities. Both stability analysis and apriori error estimates are established for common choices of numerical fluxes. We present a series of numerical experiments to confirm the optimal convergence rates for smooth solutions and its robustness in maintaining oscillation-free behavior for nonsmooth solutions in wave equations without or with nonlinear source terms.
Cite
@article{arxiv.2507.01736,
title = {An energy-based discontinuous Galerkin method for the wave equation with nonsmooth solutions},
author = {Yangxin Fu and Yan Jiang and Siyang Wang},
journal= {arXiv preprint arXiv:2507.01736},
year = {2025}
}