In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous discretisations in space, admits a local and global conservation law of energy. We also show existence and uniqueness of solutions 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 Schr\"odinger equation.

翻译：在这项工作中,我们建议为汉密尔顿群岛的多分流配方为汉密尔顿群岛的多分流式提出一个新的、任意顺序空间-时间限制元素分解。我们表明,通过在空间使用连续和不连续的分解获得的新方法承认了当地和全球的节能法。我们还显示了离散方程式解决办法的存在和独特性。此外,我们说明了在线性和非线性波方程式和非线性Schr\''odinger方程式的广泛数字实验中拟议的分解的错误行为和保存特性。