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

We study space--time isogeometric discretizations of the linear acoustic wave equation that use B-splines of arbitrary degree $p$, both in space and time. We propose a space--time variational formulation that is obtained by adding a non-consistent penalty term of order $2p+2$ to the bilinear form coming from integration by parts. This formulation, when discretized with tensor-product spline spaces with maximal regularity in time, is unconditionally stable: the mesh size in time is not constrained by the mesh size in space. We give extensive numerical evidence for the good stability, approximation, dissipation and dispersion properties of the stabilized isogeometric formulation, comparing against stabilized finite element schemes, for a range of wave propagation problems with constant and variable wave speed.