Unconditionally stable space–time isogeometric discretization for the wave equation in Hamiltonian formulation

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 Ferrari and Fraschini Math. Comput . (2025), 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.