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.