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Paper details
Number 3 - September 2017
Volume 27 - 2017
Conservative finite volume element schemes for the complex modified Korteweg–de Vries equation
Jin-Liang Yan, Liang-Hong Zheng
Abstract
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