论文标题
多核PDE的有限元离散元素的离散保护法
Discrete conservation laws for finite element discretisations of multisymplectic PDEs
论文作者
论文摘要
在这项工作中，我们提出了一个新的，任意的订单时空有限元在多胶束公式中的Hamiltonian PDES。我们表明，通过在空间中使用连续和不连续的离散来获得的新方法，承认了本地和全球的能源保护法。我们还显示了离散方程解决方案解决方案的存在和独特性。此外，我们说明了在线性和非线性波方程以及非线性schrödinger方程上进行的广泛数值实验中提出的离散化的误差行为和守恒性能。
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 Schrödinger equation.
