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Symplectic Hamiltonian finite element methods for linear elastodynamics
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-04-23 , DOI: 10.1016/j.cma.2021.113843
Manuel A. Sánchez , Bernardo Cockburn , Ngoc-Cuong Nguyen , Jaime Peraire

We present a class of high-order finite element methods that can conserve the linear and angular momenta as well as the energy for the equations of linear elastodynamics. These methods are devised by exploiting and preserving the Hamiltonian structure of the equations of linear elastodynamics. We show that several mixed finite element, discontinuous Galerkin, and hybridizable discontinuous Galerkin (HDG) methods belong to this class. We discretize the semidiscrete Hamiltonian system in time by using a symplectic integrator in order to ensure the symplectic properties of the resulting methods, which are called symplectic Hamiltonian finite element methods. For a particular semidiscrete HDG method, we obtain optimal error estimates and present, for the symplectic Hamiltonian HDG method, numerical experiments that confirm its optimal orders of convergence for all variables as well as its conservation properties.



中文翻译:

线性弹性动力学的辛辛哈密顿有限元方法

我们提出了一类高阶有限元方法,可以保留线性和角动量以及线性弹性动力学方程的能量。这些方法是通过利用和保留线性弹性动力学方程哈密​​顿结构来设计的。我们显示了几种混合有限元,不连续Galerkin和可混合不连续Galerkin(HDG)方法属于此类。我们通过使用辛积分器及时离散半离散哈密顿系统为了确保所得方法的辛性质,这些方法称为辛哈密顿有限元方法。对于特定的半离散HDG方法,我们获得了最佳误差估计,并针对辛哈密顿量HDG方法,进行了数值实验,证实了其对所有变量的最优收敛阶数以及其守恒性质。

更新日期:2021-04-23
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