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The design of conservative finite element discretisations for the vectorial modified KdV equation

Jackaman, James and Papamikos, Georgios and Pryer, Tristan (2019) 'The design of conservative finite element discretisations for the vectorial modified KdV equation.' Applied Numerical Mathematics, 137. 230 - 251. ISSN 0168-9274

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Abstract

We design a consistent Galerkin scheme for the approximation of the vectorial modified Korteweg–de Vries equation with periodic boundary conditions. We demonstrate that the scheme conserves energy up to solver tolerance. In this sense the method is consistent with the energy balance of the continuous system. This energy balance ensures there is no numerical dissipation allowing for extremely accurate long time simulations free from numerical artifacts. Various numerical experiments are shown demonstrating the asymptotic convergence of the method with respect to the discretisation parameters. Some simulations are also presented that correctly capture the unusual interactions between solitons in the vectorial setting.

Item Type: Article
Uncontrolled Keywords: Hamiltonian PDE; Conservative finite element method; Vectorial modified KdV equation
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 29 Sep 2020 15:10
Last Modified: 29 Sep 2020 15:10
URI: http://repository.essex.ac.uk/id/eprint/28761

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