English

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.

Keywords

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}
}
R2 v1 2026-06-23T13:21:26.445Z