In this paper, we propose a novel high order unfitted finite element method on Cartesian meshes for solving the acoustic wave equation with discontinuous coefficients having complex interface geometry. The unfitted finite element method does not require any penalty to achieve optimal convergence. We also introduce a new explicit time discretization method for the ODE system resulting from the spatial discretization of the wave equation. The strong stability and optimal $hp$-version error estimates both in time and space are established. Numerical examples confirm our theoretical results.
翻译:在本文中,我们建议对笛卡尔海绵采用一种新的高顺序不合格有限元素方法,用具有复杂界面几何特征的不连续系数解决声波方程式。不合格有限元素方法并不要求任何惩罚以实现最佳趋同。我们还为因波形空间分解而生成的ODE系统引入了新的明确的时间分解方法。在时间和空间方面,都建立了强大的稳定性和最佳的$hp$反向误差估计。数字例子证实了我们的理论结果。