A note on the adaptive conservative/dissipative discretization for evolutionary partial differential equations

An adaptive conservative or dissipative numerical method for nonlinear partial differential equations is established. The method not only inherits the welcome conservation or dissipation property of the equation but also uses suitable non-uniform grids at each time step. Our numerical experiments indicate that the method is useful especially for localized solutions such as solitary wave solutions. keyword Energy conservation/dissipation, Discrete gradient method, Discrete variational derivative method, Dynamic grid adaptation