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An energy-based discontinuous Galerkin method for semilinear wave equations (2001.09690v1)
Published 27 Jan 2020 in math.NA and cs.NA
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.