A high order IMEX method for generalized Korteweg de-Vries equations

In this paper, we introduce a high order space–time approximation of generalized Korteweg de-Vries equations. More specifically, the method uses continuous H 1 -conforming finite elements for the spatial approximation and implicit-explicit methods for the temporal approximation. The discretization implies the method is asymptotic preserving. The low-order variant is provably stable and mass conservative; the high-order variant is at least second-order accurate in both space and time, well-defined, and mass-conservative. The scheme is formulated, its properties are proven, and numerical simulations are provided to illustrate the proposed methodology.