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We study space--time isogeometric discretizations of the linear acoustic waveequation that use B-splines of arbitrary degree $p$, both in space and time. Wepropose a space--time variational formulation that is obtained by adding anon-consistent penalty term of order $2p+2$ to the bilinear form coming fromintegration by parts. This formulation, when discretized with tensor-productspline spaces with maximal regularity in time, is unconditionally stable: themesh size in time is not constrained by the mesh size in space. We giveextensive numerical evidence for the good stability, approximation, dissipationand dispersion properties of the stabilized isogeometric formulation, comparingagainst stabilized finite element schemes, for a range of wave propagationproblems with constant and variable wave speed.

An unconditionally stable space-time isogeometric method for the acoustic wave equation