Discrete conservation laws for finite element discretisations of multisymplectic PDEs

08/31/2020

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by   Elena Celledoni, et al.

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In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multi-symplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous discretisations in space, admits local and global conservation laws of energy and momentum. We show existence and uniqueness of solution of the discrete equations. Further, we illustrate the error behaviour and the conservation properties of the proposed discretisation in extensive numerical experiments on the linear and nonlinear wave equation and on the nonlinear Schrodinger equation.