We consider a family of conforming space-time discretizations for the wave equation based on a first-order-in-time formulation employing maximal regularity splines. In contrast with second-order-in-time formulations, which require a CFL condition to guarantee stability, the methods we consider here are unconditionally stable without the need for stabilization terms. Along the lines of the work by M. Ferrari and S. Fraschini (2024), we address the stability analysis by studying the properties of the condition number of a family of matrices associated with the time discretization. Numerical tests validate the performance of the method.

翻译：本文研究了一类基于一阶时间格式、采用最大正则样条的波动方程保形时空离散方法。与需要满足CFL条件以保证稳定性的二阶时间格式不同，本文所提方法无需稳定项即可实现无条件稳定。沿袭M. Ferrari与S. Fraschini（2024）的研究思路，我们通过分析时间离散相关矩阵族的条件数特性来探讨稳定性问题。数值实验验证了该方法的性能表现。