论文标题
针对各向异性和异质边界控制的N维波方程的结构保存空间限制的数值分析
Numerical analysis of a structure-preserving space-discretization for an anisotropic and heterogeneous boundary controlled N-dimensional wave equation as port-Hamiltonian system
论文作者
论文摘要
在边界处受控和观察到的各向异性和异质$ n $维波方程被视为港口 - 哈米尔顿港系统。采用了一种最新的结构性混合盖金方法，直接导致了有限的 - 港口港口系统：其数值分析是在一般框架中进行的。然后证明，混合有限元的最佳选择可以达到融合率和国家错误自由度的最佳折衷。确定了exta兼容性条件，使哈密顿误差是状态误差的两倍，并提供了数值证据表明有限元家族的某些组合符合这些条件。进行了2D中的数值模拟，以说明经典有限元家族的几种选择中的主要定理。提供了几种测试用例，包括非凸面结构域，各向异性或杂物病例以及吸收边界条件。
The anisotropic and heterogeneous $N$-dimensional wave equation, controlled and observed at the boundary, is considered as a port-Hamiltonian system. A recent structure-preserving mixed Galerkin method is applied, leading directly to a finite-dimensional port-Hamiltonian system: its numerical analysis is carried out in a general framework. Optimal choices of mixed finite elements are then proved to reach the best trade-off between the convergence rate and the number of degrees of freedom for the state error. Exta compatibility conditions are identified for the Hamiltonian error to be twice that of the state error, and numerical evidence is provided that some combinations of finite element families meet these conditions. Numerical simulations in 2D are performed to illustrate the main theorems among several choices of classical finite element families. Several test cases are provided, including non-convex domain, anisotropic or hetergoneous cases and absorbing boundary conditions.
