论文标题
霍奇波方程的能量保存混合有限元方法
Energy-preserving mixed finite element methods for the Hodge wave equation
论文作者
论文摘要
在本文中开发了用于求解Hodge Wave方程的能源保存数值方法。基于DE RHAM复合物，可以将Hodge Wave方程式用于一阶系统，并使用有限元外观计算进行混合有限元方法来离散空间。连续的时间盖尔金方法可以将其视为曲柄 - 尼科尔森方法的修改，用于离散时间，从而导致完整的离散方法在源项消失时准确保留能量。基于投影的运算符用于建立所提出方法的最佳订单收敛。存在数值实验以支持理论结果。
Energy-preserving numerical methods for solving the Hodge wave equation is developed in this paper. Based on the de Rham complex, the Hodge wave equation can be formulated as a first-order system and mixed finite element methods using finite element exterior calculus is used to discretize the space. A continuous time Galerkin method, which can be viewed as a modification of the Crank-Nicolson method, is used to discretize the time which results in a full discrete method preserving the energy exactly when the source term is vanished. A projection based operator is used to establish the optimal order convergence of the proposed methods. Numerical experiments are present to support the theoretical results.
