journal contribution posted on 17.06.2020 by DC Antonopoulos, VA Dougalis, Dimitrios Mitsotakis
Any type of content formally published in an academic journal, usually following a peer-review process.
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature. We consider the Camassa–Holm (CH) equation, a nonlinear dispersive wave equation that models one-way propagation of long waves of moderately small amplitude. We discretize in space the periodic initial-value problem for CH (written in its original and in system form), using the standard Galerkin finite element method with smooth splines on a uniform mesh, and prove optimal-order L2-error estimates for the semidiscrete approximation. Using the fourth-order accurate, explicit, “classical” Runge–Kutta scheme for time-stepping, we construct a highly accurate, stable, fully discrete scheme that we employ in numerical experiments to approximate solutions of CH, mainly smooth travelling waves and nonsmooth solitons of the ‘peakon’ type.
Preferred citationAntonopoulos, D.C., Dougalis, V.A. & Mitsotakis, D.E. (2019). Error estimates for Galerkin finite element methods for the Camassa–Holm equation. Numerische Mathematik, 142(4), 833-862. https://doi.org/10.1007/s00211-019-01045-7
Journal titleNumerische Mathematik
PublisherSpringer Science and Business Media LLC
Online publication date11/05/2019