Abstract
AbstractThis paper develops a high‐order discontinuous Galerkin (DG) method for the Camassa‐Holm‐Kadomtsev‐Petviashvili (CH‐KP) type equations on Cartesian meshes. The significant part of the simulation for the CH‐KP type equations lies in the treatment for the integration operator . Our proposed DG method deals with it element by element, which is efficient and applicable to most solutions. Using the instinctive energy of the original PDE as a guiding principle, the DG scheme can be proved as an energy stable numerical scheme. In addition, the semi‐discrete error estimates results for the nonlinear case are derived without any priori assumption. Several numerical experiments demonstrate the capability of our schemes for various types of solutions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Numerical Methods for Partial Differential Equations
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
