Conservative finite volume element schemes for the complex modified Korteweg-de Vries equation - Yan, Jin-Liang; Zheng, Liang-Hong (Zielona Góra: Uniwersytet Zielonogórski)
The aim of this paper is to build and validate a class of energy-preserving schemes for simulating a complex modified Korteweg-de Vries equation. The method is based on a combination of a discrete variational derivative method in time and finite volume element approximation in space. The resulting scheme is accurate, robust and energy-preserving. In addition, for comparison, we also develop a momentum-preserving finite volume element scheme and an implicit midpoint finite volume element scheme. Finally, a complete numerical study is developed to investigate the accuracy, conservation properties and long time behaviors of the energy-preserving scheme, in comparison with the momentum-preserving scheme and the implicit midpoint scheme, for the complex modified Korteweg-de Vries equation.
Keywords: mass; energy; momentum; finite volume element method; complex modified Korteweg-de Vries equation