An energy-based discontinuous Galerkin method for semilinear wave equations

Abstract We generalize the energy-based discontinuous Galerkin method proposed in [1] 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.