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A partitioned finite element method for power-preserving discretization of open systems of conservation laws
IMA Journal of Mathematical Control and Information ( IF 1.5 ) Pub Date : 2020-12-28 , DOI: 10.1093/imamci/dnaa038
Flávio Luiz Cardoso-Ribeiro 1 , Denis Matignon 2 , Laurent Lefèvre 3
Affiliation  

This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and geometries. For these systems, a partitioned finite element method (PFEM) is derived, based on the integration by parts of one of the two conservation laws written in weak form. The non-linear one-dimensional shallow-water equation (SWE) is first considered as a motivation example. Then, the method is investigated on the example of the non-linear two-dimensional SWE. Complete derivation of the reduced finite-dimensional port-Hamiltonian system (pHs) is provided and numerical experiments are performed. Extensions to curvilinear (polar) coordinate systems, space-varying coefficients and higher-order pHs (Euler–Bernoulli beam equation) are provided.

中文翻译:

开放守恒定律系统功率保持离散化的分区有限元方法

本文提出了一种用于分布式参数端口-哈密尔顿系统的结构保持空间离散化方法。所考虑的系统类别是任意空间维度和几何形状的两个守恒定律的双曲系统。对于这些系统,基于以弱形式编写的两个守恒定律之一的一部分的积分,导出了分区有限元方法 (PFEM)。非线性一维浅水方程 (SWE) 首先被视为一个动机示例。然后,以非线性二维SWE为例对该方法进行了研究。提供了简化的有限维哈密顿系统 (pH) 的完整推导,并进行了数值实验。曲线(极)坐标系的扩展,
更新日期:2020-12-28
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