An energy-based discontinuous Galerkin method for semilinear wave equations
Numerical Analysis
2020-07-15 v1 Numerical Analysis
Abstract
We generalize the energy-based discontinuous Galerkin method proposed in [SIAM J. Num. Anal., 53(6):2705-2726, 2015.] to second-order semilinear wave equations. A stability and convergence analysis is presented along with numerical experiments demonstrating optimal convergence for certain choices of the interelement fluxes. Applications to the sine-Gordon equation include simulations of breathers, kink, and anti-kink solitons.
Cite
@article{arxiv.2001.09690,
title = {An energy-based discontinuous Galerkin method for semilinear wave equations},
author = {Daniel Appelo and Thomas Hagstrom and Qi Wang and Lu Zhang},
journal= {arXiv preprint arXiv:2001.09690},
year = {2020}
}