论文标题
哈米尔顿港不连续的galerkin有限元方法
Port-Hamiltonian Discontinuous Galerkin Finite Element Methods
论文作者
论文摘要
哈米尔顿港（PH）系统制剂是一种几何概念，用于为各种物理系统制定保护法。分布式参数 - 港口 - 汉密尔顿公式模型的无限尺寸哈密顿动力系统，该系统具有非零的能量通过边界。在本文中，我们提出了一个新的pH-System不连续Galerkin（DG）离散框架的新框架。将DG方法与pH-系统联系起来会产生兼容的结构，以保留有限元离散化以及涉及变量的几何形状和功能空间的灵活性。此外，哈米尔顿港公式的配方使边界端口明确，这使得结构和功率保持数值通量的选择更加容易。我们陈述了不连续的有限元stokes-dirac结构，并在元素之间具有幂耦合，这为大型pH不连续的Galerkin离散化提供了数学框架。我们还为港口 - 哈米尔顿港不连续的Galerkin有限元法（pH-DGFEM）提供了先验误差分析。标量波方程显示了最佳的收敛速率，证明了港口 - 哈米尔顿港不连续的盖金有限元法。
A port-Hamiltonian (pH) system formulation is a geometrical notion used to formulate conservation laws for various physical systems. The distributed parameter port-Hamiltonian formulation models infinite dimensional Hamiltonian dynamical systems that have a non-zero energy flow through the boundaries. In this paper we propose a novel framework for discontinuous Galerkin (DG) discretizations of pH-systems. Linking DG methods with pH-systems gives rise to compatible structure preserving finite element discretizations along with flexibility in terms of geometry and function spaces of the variables involved. Moreover, the port-Hamiltonian formulation makes boundary ports explicit, which makes the choice of structure and power preserving numerical fluxes easier. We state the Discontinuous Finite Element Stokes-Dirac structure with a power preserving coupling between elements, which provides the mathematical framework for a large class of pH discontinuous Galerkin discretizations. We also provide an a priori error analysis for the port-Hamiltonian discontinuous Galerkin Finite Element Method (pH-DGFEM). The port-Hamiltonian discontinuous Galerkin finite element method is demonstrated for the scalar wave equation showing optimal rates of convergence.
